A299341 Number of nX4 0..1 arrays with every element equal to 0, 1, 2, 3, 5 or 8 king-move adjacent elements, with upper left element zero.

8, 88, 357, 1618, 7667, 36182, 170056, 800122, 3767186, 17734561, 83479159, 392987920, 1850012870, 8708867437, 40997169371, 192995291801, 908527255643, 4276905653092, 20133609473244, 94779278302086, 446174932260786

Offset

1,1

Comments

Column 4 of A299345.

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

Empirical: a(n) = 10*a(n-1) -37*a(n-2) +96*a(n-3) -295*a(n-4) +673*a(n-5) -909*a(n-6) +1187*a(n-7) -949*a(n-8) -2177*a(n-9) +7749*a(n-10) -19356*a(n-11) +37168*a(n-12) -52068*a(n-13) +81815*a(n-14) -105819*a(n-15) +100885*a(n-16) -113986*a(n-17) +36721*a(n-18) +143450*a(n-19) -348218*a(n-20) +1056872*a(n-21) -2401918*a(n-22) +3956877*a(n-23) -6499038*a(n-24) +10131338*a(n-25) -13384092*a(n-26) +16476162*a(n-27) -17931324*a(n-28) +15391473*a(n-29) -11736738*a(n-30) +6257415*a(n-31) +4049797*a(n-32) -12652306*a(n-33) +16700015*a(n-34) -19026560*a(n-35) +16431539*a(n-36) -12248053*a(n-37) +10852209*a(n-38) -4791298*a(n-39) -1973130*a(n-40) +1171493*a(n-41) +735865*a(n-42) -1014863*a(n-43) +1063563*a(n-44) -549240*a(n-45) +457362*a(n-46) -1087285*a(n-47) +1097896*a(n-48) -330087*a(n-49) -27646*a(n-50) +134740*a(n-51) -111077*a(n-52) +60920*a(n-53) -24680*a(n-54) +19204*a(n-55) -15442*a(n-56) -8466*a(n-57) -632*a(n-58) +2822*a(n-59) +198*a(n-60) -240*a(n-61) +608*a(n-62) -352*a(n-63) +160*a(n-64) for n>65

Example

Some solutions for n=7
..0..0..1..0. .0..0..0..0. .0..0..1..0. .0..0..1..0. .0..0..1..0
..0..1..1..1. .1..1..1..1. .0..1..1..1. .0..1..1..1. .0..1..1..1
..0..1..0..1. .0..0..0..0. .0..1..0..1. .0..1..0..1. .0..1..0..1
..0..0..0..1. .1..1..1..1. .1..0..0..1. .0..0..0..0. .0..1..0..0
..1..1..0..1. .0..0..0..0. .0..1..0..1. .0..1..1..1. .0..1..1..1
..1..1..0..1. .0..0..0..0. .0..1..1..1. .1..0..1..0. .1..0..0..0
..1..1..0..1. .0..0..0..0. .1..0..0..1. .0..1..0..1. .0..1..1..1

Crossrefs

Cf. A299345.

Sequence in context: A250276 A298191 A299085 * A299848 A299004 A299671

Adjacent sequences: A299338 A299339 A299340 * A299342 A299343 A299344

Keyword

nonn

Author

R. H. Hardin, Feb 07 2018

Status

approved