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# User:Georgi Guninski/seqs/relations1

### Relations

Some relations in a single sequence found by stefun'. ext link' is external link

A000023 ext link 4*a(n - 2)*a(n - 1) - 2*a(n - 2)*a(n + 1) + 4*a(n - 1)^2 - a(n - 1)*a(n + 1) + 3*a(n - 1)*a(n) + a(n)^2

A000023 ext link ${\displaystyle 4\,a\left(n-2\right)a\left(n-1\right)-2\,a\left(n-2\right)a\left(n+1\right)+4\,a\left(n-1\right)^{2}-a\left(n-1\right)a\left(n+1\right)+3\,a\left(n-1\right)a\left(n\right)+a\left(n\right)^{2}}$ A000030 ext link a(n - 2)*a(n + 1) - a(n - 2)*a(n) - 2*a(n - 1)*a(n + 1) + 2*a(n - 1)*a(n) + a(n + 1)*a(n) - a(n)^2

A000030 ext link ${\displaystyle a\left(n-2\right)a\left(n+1\right)-a\left(n-2\right)a\left(n\right)-2\,a\left(n-1\right)a\left(n+1\right)+2\,a\left(n-1\right)a\left(n\right)+a\left(n+1\right)a\left(n\right)-a\left(n\right)^{2}}$ A000069 ext link -1/11*a(n - 2)^2 + 1/11*a(n - 2)*a(n - 1) + 1/11*a(n - 2)*a(n) - 1/11*a(n - 1)^2 + 1/11*a(n - 1)*a(n) - 1/11*a(n)^2 - 6/11*a(n - 2) + 6/11*a(n) - 1

A000069 ext link ${\displaystyle -{\frac {1}{11}}\,a\left(n-2\right)^{2}+{\frac {1}{11}}\,a\left(n-2\right)a\left(n-1\right)+{\frac {1}{11}}\,a\left(n-2\right)a\left(n\right)-{\frac {1}{11}}\,a\left(n-1\right)^{2}+{\frac {1}{11}}\,a\left(n-1\right)a\left(n\right)-{\frac {1}{11}}\,a\left(n\right)^{2}-{\frac {6}{11}}\,a\left(n-2\right)+{\frac {6}{11}}\,a\left(n\right)-1}$ A000069 ext link -1/11*a(n - 1)^2 + 1/11*a(n - 1)*a(n + 1) + 1/11*a(n - 1)*a(n) - 1/11*a(n + 1)^2 + 1/11*a(n + 1)*a(n) - 1/11*a(n)^2 - 6/11*a(n - 1) + 6/11*a(n + 1) - 1

A000069 ext link ${\displaystyle -{\frac {1}{11}}\,a\left(n-1\right)^{2}+{\frac {1}{11}}\,a\left(n-1\right)a\left(n+1\right)+{\frac {1}{11}}\,a\left(n-1\right)a\left(n\right)-{\frac {1}{11}}\,a\left(n+1\right)^{2}+{\frac {1}{11}}\,a\left(n+1\right)a\left(n\right)-{\frac {1}{11}}\,a\left(n\right)^{2}-{\frac {6}{11}}\,a\left(n-1\right)+{\frac {6}{11}}\,a\left(n+1\right)-1}$ A000085 ext link a(n - 2)*a(n - 1) - a(n - 2)*a(n + 1) + a(n - 2)*a(n) - a(n - 1)^2 + a(n - 1)*a(n)

A000085 ext link ${\displaystyle a\left(n-2\right)a\left(n-1\right)-a\left(n-2\right)a\left(n+1\right)+a\left(n-2\right)a\left(n\right)-a\left(n-1\right)^{2}+a\left(n-1\right)a\left(n\right)}$ A000108 ext link 10*a(n - 1)*a(n + 1) - 16*a(n - 1)*a(n) - a(n + 1)*a(n) - 2*a(n)^2

A000108 ext link ${\displaystyle 10\,a\left(n-1\right)a\left(n+1\right)-16\,a\left(n-1\right)a\left(n\right)-a\left(n+1\right)a\left(n\right)-2\,a\left(n\right)^{2}}$ A000108 ext link 112*a(n - 2)*a(n + 1) - 256*a(n - 2)*a(n) - 6*a(n - 1)*a(n + 1) - a(n + 1)*a(n) - 2*a(n)^2

A000108 ext link ${\displaystyle 112\,a\left(n-2\right)a\left(n+1\right)-256\,a\left(n-2\right)a\left(n\right)-6\,a\left(n-1\right)a\left(n+1\right)-a\left(n+1\right)a\left(n\right)-2\,a\left(n\right)^{2}}$ A000108 ext link 2048/3*a(n - 2)*a(n - 1) - 560/3*a(n - 2)*a(n + 1) + 256/3*a(n - 1)^2 + 110/3*a(n - 1)*a(n + 1) - a(n + 1)*a(n) - 2*a(n)^2

A000108 ext link ${\displaystyle {\frac {2048}{3}}\,a\left(n-2\right)a\left(n-1\right)-{\frac {560}{3}}\,a\left(n-2\right)a\left(n+1\right)+{\frac {256}{3}}\,a\left(n-1\right)^{2}+{\frac {110}{3}}\,a\left(n-1\right)a\left(n+1\right)-a\left(n+1\right)a\left(n\right)-2\,a\left(n\right)^{2}}$ A000120 ext link -a(n - 2)*a(n - 1) + a(n - 2)*a(n) + a(n - 1)^2 - a(n - 1)*a(n) - a(n - 2) + a(n) - 1

A000120 ext link ${\displaystyle -a\left(n-2\right)a\left(n-1\right)+a\left(n-2\right)a\left(n\right)+a\left(n-1\right)^{2}-a\left(n-1\right)a\left(n\right)-a\left(n-2\right)+a\left(n\right)-1}$ A000120 ext link a(n - 1)*a(n + 1) - a(n - 1)*a(n) - a(n + 1)*a(n) + a(n)^2 - a(n - 1) + a(n + 1) - 1

A000120 ext link ${\displaystyle a\left(n-1\right)a\left(n+1\right)-a\left(n-1\right)a\left(n\right)-a\left(n+1\right)a\left(n\right)+a\left(n\right)^{2}-a\left(n-1\right)+a\left(n+1\right)-1}$ A000123 ext link -a(n - 2)*a(n - 1) - a(n - 2)*a(n + 1) + 2*a(n - 2)*a(n) + 2*a(n - 1)^2 + 2*a(n - 1)*a(n + 1) - 5*a(n - 1)*a(n) - a(n + 1)*a(n) + 2*a(n)^2

A000123 ext link ${\displaystyle -a\left(n-2\right)a\left(n-1\right)-a\left(n-2\right)a\left(n+1\right)+2\,a\left(n-2\right)a\left(n\right)+2\,a\left(n-1\right)^{2}+2\,a\left(n-1\right)a\left(n+1\right)-5\,a\left(n-1\right)a\left(n\right)-a\left(n+1\right)a\left(n\right)+2\,a\left(n\right)^{2}}$ A000142 ext link -a(n - 1)*a(n + 1) + a(n - 1)*a(n) + a(n)^2

A000142 ext link ${\displaystyle -a\left(n-1\right)a\left(n+1\right)+a\left(n-1\right)a\left(n\right)+a\left(n\right)^{2}}$ A000142 ext link a(n - 2)*a(n + 1) - 2*a(n - 2)*a(n) - a(n - 1)*a(n + 1) + a(n)^2

A000142 ext link ${\displaystyle a\left(n-2\right)a\left(n+1\right)-2\,a\left(n-2\right)a\left(n\right)-a\left(n-1\right)a\left(n+1\right)+a\left(n\right)^{2}}$ A000142 ext link -2*a(n - 2)*a(n - 1) + a(n - 2)*a(n + 1) - 2*a(n - 1)^2 - a(n - 1)*a(n + 1) + a(n)^2

A000142 ext link ${\displaystyle -2\,a\left(n-2\right)a\left(n-1\right)+a\left(n-2\right)a\left(n+1\right)-2\,a\left(n-1\right)^{2}-a\left(n-1\right)a\left(n+1\right)+a\left(n\right)^{2}}$ A000166 ext link a(n - 2)*a(n - 1) - a(n - 2)*a(n + 1) + a(n - 2)*a(n) + a(n - 1)^2 - a(n - 1)*a(n + 1) + 2*a(n - 1)*a(n) + a(n)^2

A000166 ext link ${\displaystyle a\left(n-2\right)a\left(n-1\right)-a\left(n-2\right)a\left(n+1\right)+a\left(n-2\right)a\left(n\right)+a\left(n-1\right)^{2}-a\left(n-1\right)a\left(n+1\right)+2\,a\left(n-1\right)a\left(n\right)+a\left(n\right)^{2}}$ A000245 ext link -16*a(n - 2)*a(n - 1) - 18*a(n - 2)*a(n + 1) + 58*a(n - 2)*a(n) - 18*a(n - 1)^2 + 13*a(n - 1)*a(n + 1) - 15*a(n - 1)*a(n) - a(n + 1)*a(n) - 3*a(n)^2

A000245 ext link ${\displaystyle -16\,a\left(n-2\right)a\left(n-1\right)-18\,a\left(n-2\right)a\left(n+1\right)+58\,a\left(n-2\right)a\left(n\right)-18\,a\left(n-1\right)^{2}+13\,a\left(n-1\right)a\left(n+1\right)-15\,a\left(n-1\right)a\left(n\right)-a\left(n+1\right)a\left(n\right)-3\,a\left(n\right)^{2}}$ A000246 ext link -a(n - 2)*a(n + 1) + 2*a(n - 2)*a(n) + a(n - 1)*a(n)

A000246 ext link ${\displaystyle -a\left(n-2\right)a\left(n+1\right)+2\,a\left(n-2\right)a\left(n\right)+a\left(n-1\right)a\left(n\right)}$ A000255 ext link a(n - 2)*a(n - 1) - a(n - 2)*a(n + 1) + 2*a(n - 2)*a(n) - a(n - 1)*a(n + 1) + 2*a(n - 1)*a(n) + a(n)^2

A000255 ext link ${\displaystyle a\left(n-2\right)a\left(n-1\right)-a\left(n-2\right)a\left(n+1\right)+2\,a\left(n-2\right)a\left(n\right)-a\left(n-1\right)a\left(n+1\right)+2\,a\left(n-1\right)a\left(n\right)+a\left(n\right)^{2}}$ A000265 ext link a(n - 2)*a(n - 1) - a(n - 2)*a(n + 1) - a(n - 1)*a(n) + a(n + 1)*a(n) + 2*a(n - 2) + 2*a(n - 1) - 2*a(n + 1) - 2*a(n) + 4

A000265 ext link ${\displaystyle a\left(n-2\right)a\left(n-1\right)-a\left(n-2\right)a\left(n+1\right)-a\left(n-1\right)a\left(n\right)+a\left(n+1\right)a\left(n\right)+2\,a\left(n-2\right)+2\,a\left(n-1\right)-2\,a\left(n+1\right)-2\,a\left(n\right)+4}$ A000378 ext link -a(n - 2)*a(n - 1) + a(n - 2)*a(n) + a(n - 1)^2 - a(n - 1)*a(n) - a(n - 2) + a(n) - 1

A000378 ext link ${\displaystyle -a\left(n-2\right)a\left(n-1\right)+a\left(n-2\right)a\left(n\right)+a\left(n-1\right)^{2}-a\left(n-1\right)a\left(n\right)-a\left(n-2\right)+a\left(n\right)-1}$ A000378 ext link a(n - 1)*a(n + 1) - a(n - 1)*a(n) - a(n + 1)*a(n) + a(n)^2 - a(n - 1) + a(n + 1) - 1

A000378 ext link ${\displaystyle a\left(n-1\right)a\left(n+1\right)-a\left(n-1\right)a\left(n\right)-a\left(n+1\right)a\left(n\right)+a\left(n\right)^{2}-a\left(n-1\right)+a\left(n+1\right)-1}$ A000389 ext link -4*a(n - 1)*a(n + 1) - a(n - 1)*a(n) - a(n + 1)*a(n) + 6*a(n)^2

A000389 ext link ${\displaystyle -4\,a\left(n-1\right)a\left(n+1\right)-a\left(n-1\right)a\left(n\right)-a\left(n+1\right)a\left(n\right)+6\,a\left(n\right)^{2}}$ A000389 ext link -3/7*a(n - 2)*a(n + 1) - 2/7*a(n - 2)*a(n) - 30/7*a(n - 1)*a(n + 1) - a(n + 1)*a(n) + 6*a(n)^2

A000389 ext link ${\displaystyle -{\frac {3}{7}}\,a\left(n-2\right)a\left(n+1\right)-{\frac {2}{7}}\,a\left(n-2\right)a\left(n\right)-{\frac {30}{7}}\,a\left(n-1\right)a\left(n+1\right)-a\left(n+1\right)a\left(n\right)+6\,a\left(n\right)^{2}}$ A000389 ext link 1/15*a(n - 2)*a(n - 1) - 2/5*a(n - 2)*a(n + 1) - 2/5*a(n - 1)^2 - 64/15*a(n - 1)*a(n + 1) - a(n + 1)*a(n) + 6*a(n)^2

A000389 ext link ${\displaystyle {\frac {1}{15}}\,a\left(n-2\right)a\left(n-1\right)-{\frac {2}{5}}\,a\left(n-2\right)a\left(n+1\right)-{\frac {2}{5}}\,a\left(n-1\right)^{2}-{\frac {64}{15}}\,a\left(n-1\right)a\left(n+1\right)-a\left(n+1\right)a\left(n\right)+6\,a\left(n\right)^{2}}$ A000522 ext link -a(n - 2)*a(n + 1) + 2*a(n - 2)*a(n) + a(n - 1)*a(n) + a(n - 2) - a(n)

A000522 ext link ${\displaystyle -a\left(n-2\right)a\left(n+1\right)+2\,a\left(n-2\right)a\left(n\right)+a\left(n-1\right)a\left(n\right)+a\left(n-2\right)-a\left(n\right)}$ A000522 ext link -a(n - 1)*a(n + 1) + a(n - 1)*a(n) + a(n)^2 + a(n - 1) - a(n)

A000522 ext link ${\displaystyle -a\left(n-1\right)a\left(n+1\right)+a\left(n-1\right)a\left(n\right)+a\left(n\right)^{2}+a\left(n-1\right)-a\left(n\right)}$ A000522 ext link a(n - 2)*a(n - 1) + a(n - 2)*a(n + 1) - 3*a(n - 2)*a(n) + a(n - 1)^2 - a(n - 1)*a(n + 1) + a(n)^2

A000522 ext link ${\displaystyle a\left(n-2\right)a\left(n-1\right)+a\left(n-2\right)a\left(n+1\right)-3\,a\left(n-2\right)a\left(n\right)+a\left(n-1\right)^{2}-a\left(n-1\right)a\left(n+1\right)+a\left(n\right)^{2}}$ A000538 ext link -847/386*a(n - 2)*a(n + 1) - 23/386*a(n - 2)*a(n) - 45/193*a(n - 1)^2 - 4065/386*a(n - 1)*a(n + 1) - 525/386*a(n - 1)*a(n) + 235/386*a(n + 1)^2 - 1034/193*a(n + 1)*a(n) + 7383/386*a(n)^2 - 14/193*a(n - 2) - 362/193*a(n + 1) - 13724/193*a(n) - 1

A000538 ext link ${\displaystyle -{\frac {847}{386}}\,a\left(n-2\right)a\left(n+1\right)-{\frac {23}{386}}\,a\left(n-2\right)a\left(n\right)-{\frac {45}{193}}\,a\left(n-1\right)^{2}-{\frac {4065}{386}}\,a\left(n-1\right)a\left(n+1\right)-{\frac {525}{386}}\,a\left(n-1\right)a\left(n\right)+{\frac {235}{386}}\,a\left(n+1\right)^{2}-{\frac {1034}{193}}\,a\left(n+1\right)a\left(n\right)+{\frac {7383}{386}}\,a\left(n\right)^{2}-{\frac {14}{193}}\,a\left(n-2\right)-{\frac {362}{193}}\,a\left(n+1\right)-{\frac {13724}{193}}\,a\left(n\right)-1}$ A000538 ext link 1/172*a(n - 2)^2 - 261/86*a(n - 2)*a(n + 1) + 25/43*a(n - 2)*a(n) - 117/172*a(n - 1)^2 - 663/43*a(n - 1)*a(n + 1) - 267/86*a(n - 1)*a(n) + 161/172*a(n + 1)^2 - 352/43*a(n + 1)*a(n) + 4971/172*a(n)^2 - 128/43*a(n + 1) - 4672/43*a(n) - 1

A000538 ext link ${\displaystyle {\frac {1}{172}}\,a\left(n-2\right)^{2}-{\frac {261}{86}}\,a\left(n-2\right)a\left(n+1\right)+{\frac {25}{43}}\,a\left(n-2\right)a\left(n\right)-{\frac {117}{172}}\,a\left(n-1\right)^{2}-{\frac {663}{43}}\,a\left(n-1\right)a\left(n+1\right)-{\frac {267}{86}}\,a\left(n-1\right)a\left(n\right)+{\frac {161}{172}}\,a\left(n+1\right)^{2}-{\frac {352}{43}}\,a\left(n+1\right)a\left(n\right)+{\frac {4971}{172}}\,a\left(n\right)^{2}-{\frac {128}{43}}\,a\left(n+1\right)-{\frac {4672}{43}}\,a\left(n\right)-1}$ A000538 ext link -175/54*a(n - 2)*a(n + 1) + 25/54*a(n - 2)*a(n) - 5/9*a(n - 1)^2 - 307/18*a(n - 1)*a(n + 1) - 7/2*a(n - 1)*a(n) + 55/54*a(n + 1)^2 - 242/27*a(n + 1)*a(n) + 191/6*a(n)^2 - 14/9*a(n - 1) - 88/27*a(n + 1) - 3170/27*a(n) - 1

A000538 ext link ${\displaystyle -{\frac {175}{54}}\,a\left(n-2\right)a\left(n+1\right)+{\frac {25}{54}}\,a\left(n-2\right)a\left(n\right)-{\frac {5}{9}}\,a\left(n-1\right)^{2}-{\frac {307}{18}}\,a\left(n-1\right)a\left(n+1\right)-{\frac {7}{2}}\,a\left(n-1\right)a\left(n\right)+{\frac {55}{54}}\,a\left(n+1\right)^{2}-{\frac {242}{27}}\,a\left(n+1\right)a\left(n\right)+{\frac {191}{6}}\,a\left(n\right)^{2}-{\frac {14}{9}}\,a\left(n-1\right)-{\frac {88}{27}}\,a\left(n+1\right)-{\frac {3170}{27}}\,a\left(n\right)-1}$ A000539 ext link 11/64*a(n - 2)*a(n - 1) + 23/32*a(n - 2)*a(n + 1) + 123/64*a(n - 2)*a(n) - 107/64*a(n - 1)^2 + 123/64*a(n - 1)*a(n + 1) - 25/16*a(n - 1)*a(n) + 11/64*a(n + 1)*a(n) - 107/64*a(n)^2 + 9/64*a(n - 2) - 489/64*a(n - 1) + 9/64*a(n + 1) - 489/64*a(n) - 1

A000539 ext link ${\displaystyle {\frac {11}{64}}\,a\left(n-2\right)a\left(n-1\right)+{\frac {23}{32}}\,a\left(n-2\right)a\left(n+1\right)+{\frac {123}{64}}\,a\left(n-2\right)a\left(n\right)-{\frac {107}{64}}\,a\left(n-1\right)^{2}+{\frac {123}{64}}\,a\left(n-1\right)a\left(n+1\right)-{\frac {25}{16}}\,a\left(n-1\right)a\left(n\right)+{\frac {11}{64}}\,a\left(n+1\right)a\left(n\right)-{\frac {107}{64}}\,a\left(n\right)^{2}+{\frac {9}{64}}\,a\left(n-2\right)-{\frac {489}{64}}\,a\left(n-1\right)+{\frac {9}{64}}\,a\left(n+1\right)-{\frac {489}{64}}\,a\left(n\right)-1}$ A000539 ext link 3/140*a(n - 2)^2 - 2/35*a(n - 2)*a(n - 1) + 67/70*a(n - 2)*a(n + 1) + 57/35*a(n - 2)*a(n) - 103/140*a(n - 1)^2 + 57/35*a(n - 1)*a(n + 1) - 187/70*a(n - 1)*a(n) + 3/140*a(n + 1)^2 - 2/35*a(n + 1)*a(n) - 103/140*a(n)^2 - 138/7*a(n - 1) - 138/7*a(n) - 1

A000539 ext link ${\displaystyle {\frac {3}{140}}\,a\left(n-2\right)^{2}-{\frac {2}{35}}\,a\left(n-2\right)a\left(n-1\right)+{\frac {67}{70}}\,a\left(n-2\right)a\left(n+1\right)+{\frac {57}{35}}\,a\left(n-2\right)a\left(n\right)-{\frac {103}{140}}\,a\left(n-1\right)^{2}+{\frac {57}{35}}\,a\left(n-1\right)a\left(n+1\right)-{\frac {187}{70}}\,a\left(n-1\right)a\left(n\right)+{\frac {3}{140}}\,a\left(n+1\right)^{2}-{\frac {2}{35}}\,a\left(n+1\right)a\left(n\right)-{\frac {103}{140}}\,a\left(n\right)^{2}-{\frac {138}{7}}\,a\left(n-1\right)-{\frac {138}{7}}\,a\left(n\right)-1}$ A000540 ext link -1/64*a(n - 2)^2 + 51/224*a(n - 2)*a(n - 1) - 143/224*a(n - 2)*a(n + 1) + 99/224*a(n - 2)*a(n) - 543/448*a(n - 1)^2 + 99/224*a(n - 1)*a(n + 1) + 393/224*a(n - 1)*a(n) - 1/64*a(n + 1)^2 + 51/224*a(n + 1)*a(n) - 543/448*a(n)^2 - 11/56*a(n - 2) - 2277/56*a(n - 1) + 11/56*a(n + 1) + 2277/56*a(n) - 1

A000540 ext link ${\displaystyle -{\frac {1}{64}}\,a\left(n-2\right)^{2}+{\frac {51}{224}}\,a\left(n-2\right)a\left(n-1\right)-{\frac {143}{224}}\,a\left(n-2\right)a\left(n+1\right)+{\frac {99}{224}}\,a\left(n-2\right)a\left(n\right)-{\frac {543}{448}}\,a\left(n-1\right)^{2}+{\frac {99}{224}}\,a\left(n-1\right)a\left(n+1\right)+{\frac {393}{224}}\,a\left(n-1\right)a\left(n\right)-{\frac {1}{64}}\,a\left(n+1\right)^{2}+{\frac {51}{224}}\,a\left(n+1\right)a\left(n\right)-{\frac {543}{448}}\,a\left(n\right)^{2}-{\frac {11}{56}}\,a\left(n-2\right)-{\frac {2277}{56}}\,a\left(n-1\right)+{\frac {11}{56}}\,a\left(n+1\right)+{\frac {2277}{56}}\,a\left(n\right)-1}$ A000579 ext link -5*a(n - 1)*a(n + 1) - a(n - 1)*a(n) - a(n + 1)*a(n) + 7*a(n)^2

A000579 ext link ${\displaystyle -5\,a\left(n-1\right)a\left(n+1\right)-a\left(n-1\right)a\left(n\right)-a\left(n+1\right)a\left(n\right)+7\,a\left(n\right)^{2}}$ A000579 ext link -1/2*a(n - 2)*a(n + 1) - 1/4*a(n - 2)*a(n) - 21/4*a(n - 1)*a(n + 1) - a(n + 1)*a(n) + 7*a(n)^2

A000579 ext link ${\displaystyle -{\frac {1}{2}}\,a\left(n-2\right)a\left(n+1\right)-{\frac {1}{4}}\,a\left(n-2\right)a\left(n\right)-{\frac {21}{4}}\,a\left(n-1\right)a\left(n+1\right)-a\left(n+1\right)a\left(n\right)+7\,a\left(n\right)^{2}}$ A000579 ext link 1/21*a(n - 2)*a(n - 1) - 10/21*a(n - 2)*a(n + 1) - 1/3*a(n - 1)^2 - 110/21*a(n - 1)*a(n + 1) - a(n + 1)*a(n) + 7*a(n)^2

A000579 ext link ${\displaystyle {\frac {1}{21}}\,a\left(n-2\right)a\left(n-1\right)-{\frac {10}{21}}\,a\left(n-2\right)a\left(n+1\right)-{\frac {1}{3}}\,a\left(n-1\right)^{2}-{\frac {110}{21}}\,a\left(n-1\right)a\left(n+1\right)-a\left(n+1\right)a\left(n\right)+7\,a\left(n\right)^{2}}$ A000580 ext link -6*a(n - 1)*a(n + 1) - a(n - 1)*a(n) - a(n + 1)*a(n) + 8*a(n)^2

A000580 ext link ${\displaystyle -6\,a\left(n-1\right)a\left(n+1\right)-a\left(n-1\right)a\left(n\right)-a\left(n+1\right)a\left(n\right)+8\,a\left(n\right)^{2}}$ A000580 ext link 4/13*a(n - 2)*a(n - 1) - 5/13*a(n - 2)*a(n + 1) + 22/13*a(n - 2)*a(n) - 32/13*a(n - 1)^2 - 80/13*a(n - 1)*a(n + 1) - a(n + 1)*a(n) + 8*a(n)^2

A000580 ext link ${\displaystyle {\frac {4}{13}}\,a\left(n-2\right)a\left(n-1\right)-{\frac {5}{13}}\,a\left(n-2\right)a\left(n+1\right)+{\frac {22}{13}}\,a\left(n-2\right)a\left(n\right)-{\frac {32}{13}}\,a\left(n-1\right)^{2}-{\frac {80}{13}}\,a\left(n-1\right)a\left(n+1\right)-a\left(n+1\right)a\left(n\right)+8\,a\left(n\right)^{2}}$ A000581 ext link -9/2*a(n - 2)*a(n - 1) + 6*a(n - 2)*a(n + 1) - 59/2*a(n - 2)*a(n) + 81/2*a(n - 1)^2 - 5*a(n - 1)*a(n + 1) - 31/2*a(n - 1)*a(n) - a(n + 1)*a(n) + 9*a(n)^2

A000581 ext link ${\displaystyle -{\frac {9}{2}}\,a\left(n-2\right)a\left(n-1\right)+6\,a\left(n-2\right)a\left(n+1\right)-{\frac {59}{2}}\,a\left(n-2\right)a\left(n\right)+{\frac {81}{2}}\,a\left(n-1\right)^{2}-5\,a\left(n-1\right)a\left(n+1\right)-{\frac {31}{2}}\,a\left(n-1\right)a\left(n\right)-a\left(n+1\right)a\left(n\right)+9\,a\left(n\right)^{2}}$ A000582 ext link -5*a(n - 2)*a(n - 1) + 7*a(n - 2)*a(n + 1) - 38*a(n - 2)*a(n) + 50*a(n - 1)^2 - 6*a(n - 1)*a(n + 1) - 17*a(n - 1)*a(n) - a(n + 1)*a(n) + 10*a(n)^2

A000582 ext link ${\displaystyle -5\,a\left(n-2\right)a\left(n-1\right)+7\,a\left(n-2\right)a\left(n+1\right)-38\,a\left(n-2\right)a\left(n\right)+50\,a\left(n-1\right)^{2}-6\,a\left(n-1\right)a\left(n+1\right)-17\,a\left(n-1\right)a\left(n\right)-a\left(n+1\right)a\left(n\right)+10\,a\left(n\right)^{2}}$ A000695 ext link -a(n - 2)*a(n - 1) + a(n - 2)*a(n) + a(n - 1)^2 - a(n - 1)*a(n) - a(n - 2) + a(n) - 1

A000695 ext link ${\displaystyle -a\left(n-2\right)a\left(n-1\right)+a\left(n-2\right)a\left(n\right)+a\left(n-1\right)^{2}-a\left(n-1\right)a\left(n\right)-a\left(n-2\right)+a\left(n\right)-1}$ A000695 ext link a(n - 1)*a(n + 1) - a(n - 1)*a(n) - a(n + 1)*a(n) + a(n)^2 - a(n - 1) + a(n + 1) - 1

A000695 ext link ${\displaystyle a\left(n-1\right)a\left(n+1\right)-a\left(n-1\right)a\left(n\right)-a\left(n+1\right)a\left(n\right)+a\left(n\right)^{2}-a\left(n-1\right)+a\left(n+1\right)-1}$ A000788 ext link -a(n - 2)*a(n - 1) - a(n - 2)*a(n + 1) + 2*a(n - 2)*a(n) + 2*a(n - 1)^2 + 2*a(n - 1)*a(n + 1) - 5*a(n - 1)*a(n) - a(n + 1)*a(n) + 2*a(n)^2 + a(n - 2) - a(n - 1) + a(n + 1) - a(n) - 1

A000788 ext link ${\displaystyle -a\left(n-2\right)a\left(n-1\right)-a\left(n-2\right)a\left(n+1\right)+2\,a\left(n-2\right)a\left(n\right)+2\,a\left(n-1\right)^{2}+2\,a\left(n-1\right)a\left(n+1\right)-5\,a\left(n-1\right)a\left(n\right)-a\left(n+1\right)a\left(n\right)+2\,a\left(n\right)^{2}+a\left(n-2\right)-a\left(n-1\right)+a\left(n+1\right)-a\left(n\right)-1}$ A000790 ext link -1/16*a(n - 2)*a(n) + 1/4*a(n - 2) + 1/4*a(n) - 1

A000790 ext link ${\displaystyle -{\frac {1}{16}}\,a\left(n-2\right)a\left(n\right)+{\frac {1}{4}}\,a\left(n-2\right)+{\frac {1}{4}}\,a\left(n\right)-1}$ A000790 ext link -1/16*a(n - 1)*a(n + 1) + 1/4*a(n - 1) + 1/4*a(n + 1) - 1

A000790 ext link ${\displaystyle -{\frac {1}{16}}\,a\left(n-1\right)a\left(n+1\right)+{\frac {1}{4}}\,a\left(n-1\right)+{\frac {1}{4}}\,a\left(n+1\right)-1}$ A000898 ext link 2*a(n - 2)*a(n - 1) - a(n - 2)*a(n + 1) + 2*a(n - 2)*a(n) - 2*a(n - 1)^2 + a(n - 1)*a(n)

A000898 ext link ${\displaystyle 2\,a\left(n-2\right)a\left(n-1\right)-a\left(n-2\right)a\left(n+1\right)+2\,a\left(n-2\right)a\left(n\right)-2\,a\left(n-1\right)^{2}+a\left(n-1\right)a\left(n\right)}$ A000957 ext link -4*a(n - 2)*a(n - 1) + 5*a(n - 2)*a(n + 1) - 11/2*a(n - 2)*a(n) - 17/2*a(n - 1)^2 + 19/2*a(n - 1)*a(n + 1) - 53/4*a(n - 1)*a(n) - a(n + 1)*a(n) - 5/2*a(n)^2

A000957 ext link ${\displaystyle -4\,a\left(n-2\right)a\left(n-1\right)+5\,a\left(n-2\right)a\left(n+1\right)-{\frac {11}{2}}\,a\left(n-2\right)a\left(n\right)-{\frac {17}{2}}\,a\left(n-1\right)^{2}+{\frac {19}{2}}\,a\left(n-1\right)a\left(n+1\right)-{\frac {53}{4}}\,a\left(n-1\right)a\left(n\right)-a\left(n+1\right)a\left(n\right)-{\frac {5}{2}}\,a\left(n\right)^{2}}$ A000984 ext link 6*a(n - 1)*a(n + 1) - 16*a(n - 1)*a(n) - a(n + 1)*a(n) + 2*a(n)^2

A000984 ext link ${\displaystyle 6\,a\left(n-1\right)a\left(n+1\right)-16\,a\left(n-1\right)a\left(n\right)-a\left(n+1\right)a\left(n\right)+2\,a\left(n\right)^{2}}$ A000984 ext link 80/3*a(n - 2)*a(n + 1) - 256/3*a(n - 2)*a(n) + 2/3*a(n - 1)*a(n + 1) - a(n + 1)*a(n) + 2*a(n)^2

A000984 ext link ${\displaystyle {\frac {80}{3}}\,a\left(n-2\right)a\left(n+1\right)-{\frac {256}{3}}\,a\left(n-2\right)a\left(n\right)+{\frac {2}{3}}\,a\left(n-1\right)a\left(n+1\right)-a\left(n+1\right)a\left(n\right)+2\,a\left(n\right)^{2}}$ A000984 ext link -2048*a(n - 2)*a(n - 1) + 240*a(n - 2)*a(n + 1) + 256*a(n - 1)^2 - 42*a(n - 1)*a(n + 1) - a(n + 1)*a(n) + 2*a(n)^2

A000984 ext link ${\displaystyle -2048\,a\left(n-2\right)a\left(n-1\right)+240\,a\left(n-2\right)a\left(n+1\right)+256\,a\left(n-1\right)^{2}-42\,a\left(n-1\right)a\left(n+1\right)-a\left(n+1\right)a\left(n\right)+2\,a\left(n\right)^{2}}$ A000999 ext link -a(n - 1)*a(n + 1) + a(n - 1)*a(n) + a(n + 1)*a(n) - a(n)^2

A000999 ext link ${\displaystyle -a\left(n-1\right)a\left(n+1\right)+a\left(n-1\right)a\left(n\right)+a\left(n+1\right)a\left(n\right)-a\left(n\right)^{2}}$ A000999 ext link a(n - 2)*a(n - 1) - a(n - 2)*a(n) - a(n - 1)^2 + a(n - 1)*a(n + 1) - a(n + 1)*a(n) + a(n)^2

A000999 ext link ${\displaystyle a\left(n-2\right)a\left(n-1\right)-a\left(n-2\right)a\left(n\right)-a\left(n-1\right)^{2}+a\left(n-1\right)a\left(n+1\right)-a\left(n+1\right)a\left(n\right)+a\left(n\right)^{2}}$ A001003 ext link -a(n - 2)*a(n - 1) - 4*a(n - 2)*a(n + 1) + 15*a(n - 2)*a(n) - 3*a(n - 1)^2 + 15*a(n - 1)*a(n + 1) - 34*a(n - 1)*a(n) - a(n + 1)*a(n) - 3*a(n)^2

A001003 ext link ${\displaystyle -a\left(n-2\right)a\left(n-1\right)-4\,a\left(n-2\right)a\left(n+1\right)+15\,a\left(n-2\right)a\left(n\right)-3\,a\left(n-1\right)^{2}+15\,a\left(n-1\right)a\left(n+1\right)-34\,a\left(n-1\right)a\left(n\right)-a\left(n+1\right)a\left(n\right)-3\,a\left(n\right)^{2}}$ A001006 ext link -9*a(n - 2)*a(n - 1) + 12*a(n - 2)*a(n + 1) - 15*a(n - 2)*a(n) + 3*a(n - 1)^2 + 5*a(n - 1)*a(n + 1) - 10*a(n - 1)*a(n) - a(n + 1)*a(n) - a(n)^2

A001006 ext link ${\displaystyle -9\,a\left(n-2\right)a\left(n-1\right)+12\,a\left(n-2\right)a\left(n+1\right)-15\,a\left(n-2\right)a\left(n\right)+3\,a\left(n-1\right)^{2}+5\,a\left(n-1\right)a\left(n+1\right)-10\,a\left(n-1\right)a\left(n\right)-a\left(n+1\right)a\left(n\right)-a\left(n\right)^{2}}$ A001040 ext link -a(n - 2)*a(n) + a(n - 1)^2 - a(n - 1)*a(n + 1) + a(n - 1)*a(n) + a(n)^2

A001040 ext link ${\displaystyle -a\left(n-2\right)a\left(n\right)+a\left(n-1\right)^{2}-a\left(n-1\right)a\left(n+1\right)+a\left(n-1\right)a\left(n\right)+a\left(n\right)^{2}}$ A001053 ext link -a(n - 2)*a(n) + a(n - 1)^2 - a(n - 1)*a(n + 1) + a(n - 1)*a(n) + a(n)^2

A001053 ext link ${\displaystyle -a\left(n-2\right)a\left(n\right)+a\left(n-1\right)^{2}-a\left(n-1\right)a\left(n+1\right)+a\left(n-1\right)a\left(n\right)+a\left(n\right)^{2}}$ A001097 ext link -1/4*a(n - 2)*a(n - 1) + 1/4*a(n - 2)*a(n) + 1/4*a(n - 1)^2 - 1/4*a(n - 1)*a(n) - 1/2*a(n - 2) + 1/2*a(n) - 1

A001097 ext link ${\displaystyle -{\frac {1}{4}}\,a\left(n-2\right)a\left(n-1\right)+{\frac {1}{4}}\,a\left(n-2\right)a\left(n\right)+{\frac {1}{4}}\,a\left(n-1\right)^{2}-{\frac {1}{4}}\,a\left(n-1\right)a\left(n\right)-{\frac {1}{2}}\,a\left(n-2\right)+{\frac {1}{2}}\,a\left(n\right)-1}$ A001097 ext link 1/4*a(n - 1)*a(n + 1) - 1/4*a(n - 1)*a(n) - 1/4*a(n + 1)*a(n) + 1/4*a(n)^2 - 1/2*a(n - 1) + 1/2*a(n + 1) - 1

A001097 ext link ${\displaystyle {\frac {1}{4}}\,a\left(n-1\right)a\left(n+1\right)-{\frac {1}{4}}\,a\left(n-1\right)a\left(n\right)-{\frac {1}{4}}\,a\left(n+1\right)a\left(n\right)+{\frac {1}{4}}\,a\left(n\right)^{2}-{\frac {1}{2}}\,a\left(n-1\right)+{\frac {1}{2}}\,a\left(n+1\right)-1}$ A001120 ext link a(n - 2)*a(n - 1) - a(n - 2)*a(n + 1) + a(n - 2)*a(n) + a(n - 1)^2 - a(n - 1)*a(n + 1) + 2*a(n - 1)*a(n) + a(n)^2

A001120 ext link ${\displaystyle a\left(n-2\right)a\left(n-1\right)-a\left(n-2\right)a\left(n+1\right)+a\left(n-2\right)a\left(n\right)+a\left(n-1\right)^{2}-a\left(n-1\right)a\left(n+1\right)+2\,a\left(n-1\right)a\left(n\right)+a\left(n\right)^{2}}$ A001193 ext link 2*a(n - 2)*a(n - 1) - a(n - 2)*a(n + 1) + 5*a(n - 2)*a(n) - a(n - 1)^2 - a(n - 1)*a(n + 1) + 3*a(n - 1)*a(n) + a(n)^2

A001193 ext link ${\displaystyle 2\,a\left(n-2\right)a\left(n-1\right)-a\left(n-2\right)a\left(n+1\right)+5\,a\left(n-2\right)a\left(n\right)-a\left(n-1\right)^{2}-a\left(n-1\right)a\left(n+1\right)+3\,a\left(n-1\right)a\left(n\right)+a\left(n\right)^{2}}$ A001287 ext link -11/2*a(n - 2)*a(n - 1) + 8*a(n - 2)*a(n + 1) - 95/2*a(n - 2)*a(n) + 121/2*a(n - 1)^2 - 7*a(n - 1)*a(n + 1) - 37/2*a(n - 1)*a(n) - a(n + 1)*a(n) + 11*a(n)^2

A001287 ext link ${\displaystyle -{\frac {11}{2}}\,a\left(n-2\right)a\left(n-1\right)+8\,a\left(n-2\right)a\left(n+1\right)-{\frac {95}{2}}\,a\left(n-2\right)a\left(n\right)+{\frac {121}{2}}\,a\left(n-1\right)^{2}-7\,a\left(n-1\right)a\left(n+1\right)-{\frac {37}{2}}\,a\left(n-1\right)a\left(n\right)-a\left(n+1\right)a\left(n\right)+11\,a\left(n\right)^{2}}$ A001288 ext link -6*a(n - 2)*a(n - 1) + 9*a(n - 2)*a(n + 1) - 58*a(n - 2)*a(n) + 72*a(n - 1)^2 - 8*a(n - 1)*a(n + 1) - 20*a(n - 1)*a(n) - a(n + 1)*a(n) + 12*a(n)^2

A001288 ext link ${\displaystyle -6\,a\left(n-2\right)a\left(n-1\right)+9\,a\left(n-2\right)a\left(n+1\right)-58\,a\left(n-2\right)a\left(n\right)+72\,a\left(n-1\right)^{2}-8\,a\left(n-1\right)a\left(n+1\right)-20\,a\left(n-1\right)a\left(n\right)-a\left(n+1\right)a\left(n\right)+12\,a\left(n\right)^{2}}$ A001297 ext link 1053/82*a(n - 2)*a(n - 1) + 43*a(n - 2)*a(n + 1) + 9011/82*a(n - 2)*a(n) - 8775/82*a(n - 1)^2 + 42213/328*a(n - 1)*a(n + 1) - 22395/328*a(n - 1)*a(n) - a(n + 1)^2 + 6889/328*a(n + 1)*a(n) - 45639/328*a(n)^2 + a(n + 1) + 1398/41*a(n)

A001297 ext link ${\displaystyle {\frac {1053}{82}}\,a\left(n-2\right)a\left(n-1\right)+43\,a\left(n-2\right)a\left(n+1\right)+{\frac {9011}{82}}\,a\left(n-2\right)a\left(n\right)-{\frac {8775}{82}}\,a\left(n-1\right)^{2}+{\frac {42213}{328}}\,a\left(n-1\right)a\left(n+1\right)-{\frac {22395}{328}}\,a\left(n-1\right)a\left(n\right)-a\left(n+1\right)^{2}+{\frac {6889}{328}}\,a\left(n+1\right)a\left(n\right)-{\frac {45639}{328}}\,a\left(n\right)^{2}+a\left(n+1\right)+{\frac {1398}{41}}\,a\left(n\right)}$ A001297 ext link 3159/5287*a(n - 2)^2 + 246295/5287*a(n - 2)*a(n + 1) + 635839/10574*a(n - 2)*a(n) - 164619/5287*a(n - 1)^2 + 2696835/21148*a(n - 1)*a(n + 1) - 1870743/21148*a(n - 1)*a(n) - a(n + 1)^2 + 433681/21148*a(n + 1)*a(n) - 2849643/21148*a(n)^2 - 18954/5287*a(n - 2) - 170586/5287*a(n - 1) + a(n + 1) + 196377/5287*a(n)

A001297 ext link ${\displaystyle {\frac {3159}{5287}}\,a\left(n-2\right)^{2}+{\frac {246295}{5287}}\,a\left(n-2\right)a\left(n+1\right)+{\frac {635839}{10574}}\,a\left(n-2\right)a\left(n\right)-{\frac {164619}{5287}}\,a\left(n-1\right)^{2}+{\frac {2696835}{21148}}\,a\left(n-1\right)a\left(n+1\right)-{\frac {1870743}{21148}}\,a\left(n-1\right)a\left(n\right)-a\left(n+1\right)^{2}+{\frac {433681}{21148}}\,a\left(n+1\right)a\left(n\right)-{\frac {2849643}{21148}}\,a\left(n\right)^{2}-{\frac {18954}{5287}}\,a\left(n-2\right)-{\frac {170586}{5287}}\,a\left(n-1\right)+a\left(n+1\right)+{\frac {196377}{5287}}\,a\left(n\right)}$ A001299 ext link -a(n - 2)*a(n - 1) + a(n - 2)*a(n + 1) + a(n - 1)^2 - a(n - 1)*a(n + 1)

A001299 ext link ${\displaystyle -a\left(n-2\right)a\left(n-1\right)+a\left(n-2\right)a\left(n+1\right)+a\left(n-1\right)^{2}-a\left(n-1\right)a\left(n+1\right)}$ A001299 ext link a(n - 2)*a(n + 1) - a(n - 2)*a(n) - a(n + 1)*a(n) + a(n)^2

A001299 ext link ${\displaystyle a\left(n-2\right)a\left(n+1\right)-a\left(n-2\right)a\left(n\right)-a\left(n+1\right)a\left(n\right)+a\left(n\right)^{2}}$ A001299 ext link a(n - 1)*a(n + 1) - a(n - 1)*a(n) - a(n + 1)*a(n) + a(n)^2

A001299 ext link ${\displaystyle a\left(n-1\right)a\left(n+1\right)-a\left(n-1\right)a\left(n\right)-a\left(n+1\right)a\left(n\right)+a\left(n\right)^{2}}$ A001300 ext link -a(n - 2)*a(n - 1) + a(n - 2)*a(n + 1) + a(n - 1)^2 - a(n - 1)*a(n + 1)

A001300 ext link ${\displaystyle -a\left(n-2\right)a\left(n-1\right)+a\left(n-2\right)a\left(n+1\right)+a\left(n-1\right)^{2}-a\left(n-1\right)a\left(n+1\right)}$ A001300 ext link a(n - 2)*a(n + 1) - a(n - 2)*a(n) - a(n + 1)*a(n) + a(n)^2

A001300 ext link ${\displaystyle a\left(n-2\right)a\left(n+1\right)-a\left(n-2\right)a\left(n\right)-a\left(n+1\right)a\left(n\right)+a\left(n\right)^{2}}$ A001300 ext link a(n - 1)*a(n + 1) - a(n - 1)*a(n) - a(n + 1)*a(n) + a(n)^2

A001300 ext link ${\displaystyle a\left(n-1\right)a\left(n+1\right)-a\left(n-1\right)a\left(n\right)-a\left(n+1\right)a\left(n\right)+a\left(n\right)^{2}}$ A001316 ext link -a(n - 1)*a(n + 1) + 2*a(n - 1)*a(n) + 1/2*a(n + 1)*a(n) - a(n)^2

A001316 ext link ${\displaystyle -a\left(n-1\right)a\left(n+1\right)+2\,a\left(n-1\right)a\left(n\right)+{\frac {1}{2}}\,a\left(n+1\right)a\left(n\right)-a\left(n\right)^{2}}$ A001316 ext link 16*a(n - 2)*a(n - 1) - 8*a(n - 2)*a(n) - 8*a(n - 1)^2 + 2*a(n - 1)*a(n + 1) - a(n + 1)*a(n) + 2*a(n)^2

A001316 ext link ${\displaystyle 16\,a\left(n-2\right)a\left(n-1\right)-8\,a\left(n-2\right)a\left(n\right)-8\,a\left(n-1\right)^{2}+2\,a\left(n-1\right)a\left(n+1\right)-a\left(n+1\right)a\left(n\right)+2\,a\left(n\right)^{2}}$ A001317 ext link -a(n - 1)*a(n + 1) + 3*a(n - 1)*a(n) + 1/3*a(n + 1)*a(n) - a(n)^2

A001317 ext link ${\displaystyle -a\left(n-1\right)a\left(n+1\right)+3\,a\left(n-1\right)a\left(n\right)+{\frac {1}{3}}\,a\left(n+1\right)a\left(n\right)-a\left(n\right)^{2}}$ A001317 ext link 81*a(n - 2)*a(n - 1) - 27*a(n - 2)*a(n) - 27*a(n - 1)^2 + 3*a(n - 1)*a(n + 1) - a(n + 1)*a(n) + 3*a(n)^2

A001317 ext link ${\displaystyle 81\,a\left(n-2\right)a\left(n-1\right)-27\,a\left(n-2\right)a\left(n\right)-27\,a\left(n-1\right)^{2}+3\,a\left(n-1\right)a\left(n+1\right)-a\left(n+1\right)a\left(n\right)+3\,a\left(n\right)^{2}}$ A001339 ext link a(n - 2)*a(n - 1) + a(n - 2)*a(n + 1) - 4*a(n - 2)*a(n) + 2*a(n - 1)^2 - a(n - 1)*a(n + 1) + a(n)^2

A001339 ext link ${\displaystyle a\left(n-2\right)a\left(n-1\right)+a\left(n-2\right)a\left(n+1\right)-4\,a\left(n-2\right)a\left(n\right)+2\,a\left(n-1\right)^{2}-a\left(n-1\right)a\left(n+1\right)+a\left(n\right)^{2}}$ A001399 ext link -a(n - 2)^2 + 2*a(n - 2)*a(n - 1) - 2*a(n - 2)*a(n + 1) + 2*a(n - 2)*a(n) - a(n - 1)^2 + 2*a(n - 1)*a(n + 1) - 2*a(n - 1)*a(n) - a(n + 1)^2 + 2*a(n + 1)*a(n) - a(n)^2 + a(n - 2) - a(n - 1) + a(n + 1) - a(n)

A001399 ext link ${\displaystyle -a\left(n-2\right)^{2}+2\,a\left(n-2\right)a\left(n-1\right)-2\,a\left(n-2\right)a\left(n+1\right)+2\,a\left(n-2\right)a\left(n\right)-a\left(n-1\right)^{2}+2\,a\left(n-1\right)a\left(n+1\right)-2\,a\left(n-1\right)a\left(n\right)-a\left(n+1\right)^{2}+2\,a\left(n+1\right)a\left(n\right)-a\left(n\right)^{2}+a\left(n-2\right)-a\left(n-1\right)+a\left(n+1\right)-a\left(n\right)}$ A001405 ext link 2*a(n - 1)*a(n + 1) - 4*a(n - 1)*a(n) - a(n + 1)*a(n) + 2*a(n)^2

A001405 ext link ${\displaystyle 2\,a\left(n-1\right)a\left(n+1\right)-4\,a\left(n-1\right)a\left(n\right)-a\left(n+1\right)a\left(n\right)+2\,a\left(n\right)^{2}}$ A001405 ext link 12*a(n - 2)*a(n + 1) - 16*a(n - 2)*a(n) - 2*a(n - 1)*a(n + 1) - a(n + 1)*a(n) + 2*a(n)^2

A001405 ext link ${\displaystyle 12\,a\left(n-2\right)a\left(n+1\right)-16\,a\left(n-2\right)a\left(n\right)-2\,a\left(n-1\right)a\left(n+1\right)-a\left(n+1\right)a\left(n\right)+2\,a\left(n\right)^{2}}$ A001405 ext link 32*a(n - 2)*a(n - 1) - 12*a(n - 2)*a(n + 1) - 16*a(n - 1)^2 + 6*a(n - 1)*a(n + 1) - a(n + 1)*a(n) + 2*a(n)^2

A001405 ext link ${\displaystyle 32\,a\left(n-2\right)a\left(n-1\right)-12\,a\left(n-2\right)a\left(n+1\right)-16\,a\left(n-1\right)^{2}+6\,a\left(n-1\right)a\left(n+1\right)-a\left(n+1\right)a\left(n\right)+2\,a\left(n\right)^{2}}$ A001476 ext link -a(n - 1)*a(n + 1) + a(n - 1)*a(n) + a(n + 1)*a(n) - a(n)^2 + a(n - 1) - a(n + 1) + 1

A001476 ext link ${\displaystyle -a\left(n-1\right)a\left(n+1\right)+a\left(n-1\right)a\left(n\right)+a\left(n+1\right)a\left(n\right)-a\left(n\right)^{2}+a\left(n-1\right)-a\left(n+1\right)+1}$ A001476 ext link -1/2*a(n - 2)*a(n + 1) + 1/2*a(n - 2)*a(n) + 1/2*a(n + 1)*a(n) - 1/2*a(n)^2 + 1/2*a(n - 2) - a(n + 1) + 1/2*a(n) + 1

A001476 ext link ${\displaystyle -{\frac {1}{2}}\,a\left(n-2\right)a\left(n+1\right)+{\frac {1}{2}}\,a\left(n-2\right)a\left(n\right)+{\frac {1}{2}}\,a\left(n+1\right)a\left(n\right)-{\frac {1}{2}}\,a\left(n\right)^{2}+{\frac {1}{2}}\,a\left(n-2\right)-a\left(n+1\right)+{\frac {1}{2}}\,a\left(n\right)+1}$ A001476 ext link a(n - 2)*a(n - 1) + a(n - 2)*a(n + 1) - 2*a(n - 2)*a(n) - a(n - 1)^2 + a(n - 1)*a(n) - a(n + 1)*a(n) + a(n)^2 + 2*a(n + 1) - 2*a(n) - 1

A001476 ext link ${\displaystyle a\left(n-2\right)a\left(n-1\right)+a\left(n-2\right)a\left(n+1\right)-2\,a\left(n-2\right)a\left(n\right)-a\left(n-1\right)^{2}+a\left(n-1\right)a\left(n\right)-a\left(n+1\right)a\left(n\right)+a\left(n\right)^{2}+2\,a\left(n+1\right)-2\,a\left(n\right)-1}$ A001492 ext link a(n - 2)*a(n + 1) - a(n - 2) - a(n + 1) + 1

A001492 ext link ${\displaystyle a\left(n-2\right)a\left(n+1\right)-a\left(n-2\right)-a\left(n+1\right)+1}$ A001492 ext link -a(n - 1)*a(n + 1) + a(n - 1) + a(n + 1) - 1

A001492 ext link ${\displaystyle -a\left(n-1\right)a\left(n+1\right)+a\left(n-1\right)+a\left(n+1\right)-1}$ A001492 ext link a(n + 1)*a(n) - a(n + 1) - a(n) + 1

A001492 ext link ${\displaystyle a\left(n+1\right)a\left(n\right)-a\left(n+1\right)-a\left(n\right)+1}$ A001511 ext link -a(n - 2)*a(n + 1) + a(n - 2) + a(n + 1) - 1

A001511 ext link ${\displaystyle -a\left(n-2\right)a\left(n+1\right)+a\left(n-2\right)+a\left(n+1\right)-1}$ A001511 ext link a(n - 1)*a(n) - a(n + 1)*a(n) - a(n - 1) + a(n + 1)

A001511 ext link ${\displaystyle a\left(n-1\right)a\left(n\right)-a\left(n+1\right)a\left(n\right)-a\left(n-1\right)+a\left(n+1\right)}$ A001511 ext link a(n - 2)*a(n - 1) - a(n - 2)*a(n + 1) - a(n - 1)*a(n) + a(n + 1)*a(n)

A001511 ext link ${\displaystyle a\left(n-2\right)a\left(n-1\right)-a\left(n-2\right)a\left(n+1\right)-a\left(n-1\right)a\left(n\right)+a\left(n+1\right)a\left(n\right)}$ A001540 ext link -1/4*a(n - 2)*a(n - 1) + 1/4*a(n - 2)*a(n + 1) - 1/4*a(n - 2)*a(n) - 1/4*a(n - 1)^2 + 1/4*a(n - 1)*a(n + 1) - 1/2*a(n - 1)*a(n) - 1/4*a(n)^2 - 1/2*a(n - 2) - a(n - 1) + 1/2*a(n + 1) - a(n) - 1

A001540 ext link ${\displaystyle -{\frac {1}{4}}\,a\left(n-2\right)a\left(n-1\right)+{\frac {1}{4}}\,a\left(n-2\right)a\left(n+1\right)-{\frac {1}{4}}\,a\left(n-2\right)a\left(n\right)-{\frac {1}{4}}\,a\left(n-1\right)^{2}+{\frac {1}{4}}\,a\left(n-1\right)a\left(n+1\right)-{\frac {1}{2}}\,a\left(n-1\right)a\left(n\right)-{\frac {1}{4}}\,a\left(n\right)^{2}-{\frac {1}{2}}\,a\left(n-2\right)-a\left(n-1\right)+{\frac {1}{2}}\,a\left(n+1\right)-a\left(n\right)-1}$ A001700 ext link 6*a(n - 1)*a(n + 1) - 16*a(n - 1)*a(n) - a(n + 1)*a(n) + 2*a(n)^2

A001700 ext link ${\displaystyle 6\,a\left(n-1\right)a\left(n+1\right)-16\,a\left(n-1\right)a\left(n\right)-a\left(n+1\right)a\left(n\right)+2\,a\left(n\right)^{2}}$ A001700 ext link 80/3*a(n - 2)*a(n + 1) - 256/3*a(n - 2)*a(n) + 2/3*a(n - 1)*a(n + 1) - a(n + 1)*a(n) + 2*a(n)^2

A001700 ext link ${\displaystyle {\frac {80}{3}}\,a\left(n-2\right)a\left(n+1\right)-{\frac {256}{3}}\,a\left(n-2\right)a\left(n\right)+{\frac {2}{3}}\,a\left(n-1\right)a\left(n+1\right)-a\left(n+1\right)a\left(n\right)+2\,a\left(n\right)^{2}}$ A001700 ext link -2048*a(n - 2)*a(n - 1) + 240*a(n - 2)*a(n + 1) + 256*a(n - 1)^2 - 42*a(n - 1)*a(n + 1) - a(n + 1)*a(n) + 2*a(n)^2

A001700 ext link ${\displaystyle -2048\,a\left(n-2\right)a\left(n-1\right)+240\,a\left(n-2\right)a\left(n+1\right)+256\,a\left(n-1\right)^{2}-42\,a\left(n-1\right)a\left(n+1\right)-a\left(n+1\right)a\left(n\right)+2\,a\left(n\right)^{2}}$ A001768 ext link -a(n - 2)*a(n - 1) - a(n - 2)*a(n + 1) + 2*a(n - 2)*a(n) + 2*a(n - 1)^2 + 2*a(n - 1)*a(n + 1) - 5*a(n - 1)*a(n) - a(n + 1)*a(n) + 2*a(n)^2

A001768 ext link ${\displaystyle -a\left(n-2\right)a\left(n-1\right)-a\left(n-2\right)a\left(n+1\right)+2\,a\left(n-2\right)a\left(n\right)+2\,a\left(n-1\right)^{2}+2\,a\left(n-1\right)a\left(n+1\right)-5\,a\left(n-1\right)a\left(n\right)-a\left(n+1\right)a\left(n\right)+2\,a\left(n\right)^{2}}$ A001768 ext link 177/43*a(n - 1)^2 + 134/43*a(n - 1)*a(n + 1) - 483/43*a(n - 1)*a(n) - a(n + 1)^2 - a(n + 1)*a(n) + 6*a(n)^2 + 593/43*a(n - 1) + 593/43*a(n + 1) - 1186/43*a(n)

A001768 ext link ${\displaystyle {\frac {177}{43}}\,a\left(n-1\right)^{2}+{\frac {134}{43}}\,a\left(n-1\right)a\left(n+1\right)-{\frac {483}{43}}\,a\left(n-1\right)a\left(n\right)-a\left(n+1\right)^{2}-a\left(n+1\right)a\left(n\right)+6\,a\left(n\right)^{2}+{\frac {593}{43}}\,a\left(n-1\right)+{\frac {593}{43}}\,a\left(n+1\right)-{\frac {1186}{43}}\,a\left(n\right)}$ A001768 ext link 8413/3997*a(n - 2)^2 + 59/14*a(n - 2)*a(n + 1) - 33297/3997*a(n - 2)*a(n) + 37/3997*a(n - 1)^2 - a(n - 1)*a(n + 1) + 8065/7994*a(n - 1)*a(n) - a(n + 1)^2 - a(n + 1)*a(n) + 15961/3997*a(n)^2 + 86/7*a(n - 2) + 172/7*a(n + 1) - 258/7*a(n)

A001768 ext link ${\displaystyle {\frac {8413}{3997}}\,a\left(n-2\right)^{2}+{\frac {59}{14}}\,a\left(n-2\right)a\left(n+1\right)-{\frac {33297}{3997}}\,a\left(n-2\right)a\left(n\right)+{\frac {37}{3997}}\,a\left(n-1\right)^{2}-a\left(n-1\right)a\left(n+1\right)+{\frac {8065}{7994}}\,a\left(n-1\right)a\left(n\right)-a\left(n+1\right)^{2}-a\left(n+1\right)a\left(n\right)+{\frac {15961}{3997}}\,a\left(n\right)^{2}+{\frac {86}{7}}\,a\left(n-2\right)+{\frac {172}{7}}\,a\left(n+1\right)-{\frac {258}{7}}\,a\left(n\right)}$ A001847 ext link 6/11*a(n - 2)*a(n - 1) - 1/11*a(n - 2)*a(n + 1) - 5*a(n - 2)*a(n) - 3/5*a(n - 1)*a(n + 1) + 63/5*a(n - 1)*a(n) - a(n + 1)^2 + 338/55*a(n + 1)*a(n) - 63/5*a(n)^2 - 16*a(n + 1) + 176*a(n)

A001847 ext link ${\displaystyle {\frac {6}{11}}\,a\left(n-2\right)a\left(n-1\right)-{\frac {1}{11}}\,a\left(n-2\right)a\left(n+1\right)-5\,a\left(n-2\right)a\left(n\right)-{\frac {3}{5}}\,a\left(n-1\right)a\left(n+1\right)+{\frac {63}{5}}\,a\left(n-1\right)a\left(n\right)-a\left(n+1\right)^{2}+{\frac {338}{55}}\,a\left(n+1\right)a\left(n\right)-{\frac {63}{5}}\,a\left(n\right)^{2}-16\,a\left(n+1\right)+176\,a\left(n\right)}$ A001847 ext link a(n - 2)*a(n + 1) - 11*a(n - 2)*a(n) + 6*a(n - 1)^2 - 33/5*a(n - 1)*a(n + 1) + 63/5*a(n - 1)*a(n) - a(n + 1)^2 + 28/5*a(n + 1)*a(n) - 33/5*a(n)^2 - 16*a(n + 1) + 176*a(n)

A001847 ext link ${\displaystyle a\left(n-2\right)a\left(n+1\right)-11\,a\left(n-2\right)a\left(n\right)+6\,a\left(n-1\right)^{2}-{\frac {33}{5}}\,a\left(n-1\right)a\left(n+1\right)+{\frac {63}{5}}\,a\left(n-1\right)a\left(n\right)-a\left(n+1\right)^{2}+{\frac {28}{5}}\,a\left(n+1\right)a\left(n\right)-{\frac {33}{5}}\,a\left(n\right)^{2}-16\,a\left(n+1\right)+176\,a\left(n\right)}$ A001847 ext link -11/4800*a(n - 2)*a(n + 1) + 1/4800*a(n - 2)*a(n) - 7/1600*a(n - 1)*a(n + 1) - 3/1600*a(n - 1)*a(n) + 1/960*a(n + 1)^2 - 7/1200*a(n + 1)*a(n) + 21/1600*a(n)^2 - 1/20*a(n - 2) + 1/4*a(n - 1) + 1/15*a(n + 1) - 13/30*a(n) - 1

A001847 ext link ${\displaystyle -{\frac {11}{4800}}\,a\left(n-2\right)a\left(n+1\right)+{\frac {1}{4800}}\,a\left(n-2\right)a\left(n\right)-{\frac {7}{1600}}\,a\left(n-1\right)a\left(n+1\right)-{\frac {3}{1600}}\,a\left(n-1\right)a\left(n\right)+{\frac {1}{960}}\,a\left(n+1\right)^{2}-{\frac {7}{1200}}\,a\left(n+1\right)a\left(n\right)+{\frac {21}{1600}}\,a\left(n\right)^{2}-{\frac {1}{20}}\,a\left(n-2\right)+{\frac {1}{4}}\,a\left(n-1\right)+{\frac {1}{15}}\,a\left(n+1\right)-{\frac {13}{30}}\,a\left(n\right)-1}$