A317600 Number of nX4 0..1 arrays with every element unequal to 0, 1, 2, 3, 5, 6, 7 or 8 king-move adjacent elements, with upper left element zero.

8, 65, 435, 3047, 20805, 143866, 994993, 6892556, 47747495, 330696013, 2290523877, 15865339426, 109889859960, 761143341606, 5272010289643, 36516212627935, 252926973440552, 1751881144044050, 12134283040744869, 84047266827333127

Offset

1,1

Comments

Column 4 of A317604.

Links

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

Formula

Empirical: a(n) = 9*a(n-1) -14*a(n-2) +30*a(n-3) -237*a(n-4) -3*a(n-5) +302*a(n-6) +1662*a(n-7) +2290*a(n-8) +955*a(n-9) -9368*a(n-10) -9888*a(n-11) +902*a(n-12) -52619*a(n-13) +12475*a(n-14) -95579*a(n-15) -114315*a(n-16) +236073*a(n-17) +543992*a(n-18) +999845*a(n-19) +1459543*a(n-20) +611564*a(n-21) -384923*a(n-22) -556857*a(n-23) -3259047*a(n-24) -1956731*a(n-25) -11545488*a(n-26) -6902245*a(n-27) -14112532*a(n-28) -16003389*a(n-29) +6245021*a(n-30) -25134138*a(n-31) -4827154*a(n-32) +6290458*a(n-33) +12260605*a(n-34) -9136962*a(n-35) +25045115*a(n-36) +31879347*a(n-37) -19656317*a(n-38) +68998896*a(n-39) +12779960*a(n-40) +9965538*a(n-41) +26731245*a(n-42) +14778589*a(n-43) -1608957*a(n-44) +1790187*a(n-45) +1466332*a(n-46) -8287569*a(n-47) +3181384*a(n-48) -4824429*a(n-49) -1563204*a(n-50) -2147248*a(n-51) -452967*a(n-52) +764876*a(n-53) -189090*a(n-54) +45732*a(n-55) -62688*a(n-56) +960*a(n-57) for n>59

Example

Some solutions for n=5
..0..1..1..1. .0..0..0..0. .0..1..1..0. .0..0..0..1. .0..1..0..1
..1..0..1..0. .0..0..0..0. .1..0..1..0. .1..0..1..1. .1..1..0..0
..0..1..1..1. .0..0..0..0. .1..0..0..0. .1..1..1..1. .1..1..1..0
..1..0..1..1. .1..0..1..0. .1..1..1..0. .1..1..1..0. .1..1..1..1
..1..1..0..0. .0..0..0..1. .0..0..0..1. .0..1..1..1. .0..1..1..1

Crossrefs

Cf. A317604.

Sequence in context: A317007 A293802 A316872 * A288788 A033118 A033126

Adjacent sequences: A317597 A317598 A317599 * A317601 A317602 A317603

Keyword

nonn

Author

R. H. Hardin, Aug 01 2018

Status

approved