A196633 Number of nX5 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 1,3,2,0,4 for x=0,1,2,3,4

1, 26, 232, 1927, 17278, 152925, 1339251, 11820065, 103936104, 915486074, 8060380033, 70961333274, 624782246290, 5500794059044, 48430956386897, 426402612324896, 3754196939727200, 33053273003024306, 291012538839640625

Offset

1,2

Comments

Every 0 is next to 0 1's, every 1 is next to 1 3's, every 2 is next to 2 2's, every 3 is next to 3 0's, every 4 is next to 4 4's

Column 5 of A196636

Links

R. H. Hardin, Table of n, a(n) for n = 1..200

Formula

Empirical: a(n) = 7*a(n-1) +14*a(n-2) +23*a(n-3) +108*a(n-4) -800*a(n-5) -4864*a(n-6) -2094*a(n-7) -19960*a(n-8) -218911*a(n-9) -145923*a(n-10) +782190*a(n-11) -1092492*a(n-12) -1579467*a(n-13) +8785126*a(n-14) +5356216*a(n-15) -18906735*a(n-16) -5226019*a(n-17) +23778322*a(n-18) -196164476*a(n-19) -87104733*a(n-20) +396889956*a(n-21) +583754189*a(n-22) +259781800*a(n-23) +464661745*a(n-24) +1720352225*a(n-25) -3845824191*a(n-26) -1133420960*a(n-27) -471934745*a(n-28) +7260522509*a(n-29) -9271193409*a(n-30) +3383084320*a(n-31) -1261295378*a(n-32) -20633451171*a(n-33) -5169759873*a(n-34) -29633311071*a(n-35) +22355993959*a(n-36) +24377755497*a(n-37) +31498209056*a(n-38) +18608823081*a(n-39) +24333413010*a(n-40) +44533873358*a(n-41) +2615133302*a(n-42) -42879811360*a(n-43) -34356004198*a(n-44) +7076269072*a(n-45) +10955597176*a(n-46) -20082403730*a(n-47) -25881805383*a(n-48) -9191202220*a(n-49) -11493764498*a(n-50) +1428032717*a(n-51) -2650075733*a(n-52) +1599255973*a(n-53) +1713937870*a(n-54) +1693346057*a(n-55) +540050407*a(n-56) +250809522*a(n-57) +71759510*a(n-58) +52165634*a(n-59) +20611354*a(n-60) +5124726*a(n-61) +14243092*a(n-62) -932988*a(n-63) -238712*a(n-64) +398452*a(n-65) -168040*a(n-66) -6800*a(n-67) -6144*a(n-68) -4352*a(n-69) for n>70

Example

Some solutions for n=4
..0..0..0..0..0....0..0..0..3..0....0..0..2..2..2....0..3..0..3..0
..0..0..3..3..0....0..0..0..0..0....0..0..2..0..2....0..0..0..0..3
..3..0..0..0..3....2..2..3..0..3....3..0..2..2..2....0..0..3..3..0
..0..3..0..3..0....2..2..0..3..0....0..3..0..0..0....0..3..0..0..0

Crossrefs

Sequence in context: A110486 A098994 A172124 * A196638 A163726 A293614

Adjacent sequences: A196630 A196631 A196632 * A196634 A196635 A196636

Keyword

nonn

Author

R. H. Hardin Oct 04 2011

Status

approved