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 A250611 T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing x(i,j)-x(i-1,j) in the j direction 8
 11, 26, 26, 57, 64, 57, 120, 140, 140, 120, 247, 290, 297, 290, 247, 502, 586, 592, 592, 586, 502, 1013, 1172, 1153, 1126, 1153, 1172, 1013, 2036, 2336, 2236, 2092, 2092, 2236, 2336, 2036, 4083, 4654, 4353, 3890, 3691, 3890, 4353, 4654, 4083, 8178, 9278 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Table starts ...11....26....57...120...247....502...1013...2036...4083...8178..16369...32752 ...26....64...140...290...586...1172...2336...4654...9278..18512..36964...73850 ...57...140...297...592..1153...2236...4353...8528..16809..33292..66169..131824 ..120...290...592..1126..2092...3890...7320..13982..27076..53002.104560..207350 ..247...586..1153..2092..3691...6526..11749..21664..40879..78610.153289..301780 ..502..1172..2236..3890..6526..10928..18664..32870..59818.112052.214660..417818 .1013..2336..4353..7320.11749..18664..30113..50192..87093.157200.293281..560872 .2036..4654..8528.13982.21664..32870..50192..78814.129104.221798.398368..741758 .4083..9278.16809.27076.40879..59818..87093.129104.198651.321334.548353..982108 .8178.18512.33292.53002.78610.112052.157200.221798.321334.486784.780100.1325186 LINKS R. H. Hardin, Table of n, a(n) for n = 1..881 FORMULA Empirical: T(n,k) = 2^(n-1)*((k+1)*2)^2 + a quadratic polynomial in n Empirical for column k (k=2 recurrence also works for k=1): k=1: a(n) = 4*a(n-1) -5*a(n-2) +2*a(n-3); a(n)=16*2^(n-1) -n-4 k=2: a(n) = 5*a(n-1) -9*a(n-2) +7*a(n-3) -2*a(n-4); a(n)=36*2^(n-1) +n^2-n-10 k=3: a(n) = 5*a(n-1) -9*a(n-2) +7*a(n-3) -2*a(n-4); a(n)=64*2^(n-1) +5*n^2+4*n-16 k=4: a(n) = 5*a(n-1) -9*a(n-2) +7*a(n-3) -2*a(n-4); a(n)=100*2^(n-1) +16*n^2+22*n-18 k=5: a(n) = 5*a(n-1) -9*a(n-2) +7*a(n-3) -2*a(n-4); a(n)=144*2^(n-1) +42*n^2+69*n-8 k=6: a(n) = 5*a(n-1) -9*a(n-2) +7*a(n-3) -2*a(n-4); a(n)=196*2^(n-1) +99*n^2+177*n+30 k=7: a(n) = 5*a(n-1) -9*a(n-2) +7*a(n-3) -2*a(n-4); a(n)=256*2^(n-1) +219*n^2+410*n+128 Empirical for diagonal: a(n) = 11*a(n-1) -52*a(n-2) +138*a(n-3) -225*a(n-4) +231*a(n-5) -146*a(n-6) +52*a(n-7) -8*a(n-8) EXAMPLE Some solutions for n=6 k=4 ..1..1..0..0..0....1..1..1..0..0....1..1..1..1..0....0..0..0..1..0 ..1..1..0..0..0....1..1..1..1..1....1..1..1..1..0....0..0..0..1..0 ..1..1..0..0..0....1..1..1..1..1....1..1..1..1..0....0..0..0..1..0 ..0..0..0..0..0....1..1..1..1..1....1..1..1..1..0....0..0..0..1..0 ..0..1..1..1..1....1..1..1..1..1....1..1..1..1..0....0..0..0..1..0 ..0..1..1..1..1....0..0..0..1..1....1..1..1..1..0....0..0..0..1..0 ..0..1..1..1..1....0..0..0..1..1....0..1..1..1..1....0..0..0..1..0 CROSSREFS Column 1 is A000295(n+3) Sequence in context: A220434 A191720 A066956 * A137015 A260903 A316315 Adjacent sequences:  A250608 A250609 A250610 * A250612 A250613 A250614 KEYWORD nonn,tabl AUTHOR R. H. Hardin, Nov 26 2014 STATUS approved

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Last modified May 18 22:37 EDT 2022. Contains 353826 sequences. (Running on oeis4.)