A299685 Number of nX4 0..1 arrays with every element equal to 0, 1, 3, 4, 5, 6 or 7 king-move adjacent elements, with upper left element zero.

5, 16, 54, 648, 2850, 20882, 159324, 1041908, 7459468, 53904306, 375940431, 2678988639, 19089395160, 135035259385, 959911426013, 6820922367039, 48396544732963, 343770481230580, 2441462845433685, 17334264880163647

Offset

1,1

Comments

Column 4 of A299689.

Links

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

Formula

Empirical: a(n) = 5*a(n-1) +20*a(n-2) +81*a(n-3) -653*a(n-4) -1905*a(n-5) +643*a(n-6) +23079*a(n-7) +48432*a(n-8) -58518*a(n-9) -346722*a(n-10) -472191*a(n-11) +736590*a(n-12) +2550808*a(n-13) +1321038*a(n-14) -4101790*a(n-15) -7503804*a(n-16) +3021497*a(n-17) +8448688*a(n-18) -3562570*a(n-19) -11841484*a(n-20) +15048149*a(n-21) +38007941*a(n-22) -4122652*a(n-23) -77892088*a(n-24) -44675826*a(n-25) +53117546*a(n-26) +92005643*a(n-27) +31709255*a(n-28) -62292123*a(n-29) -90295223*a(n-30) -9746620*a(n-31) +70199783*a(n-32) +51756737*a(n-33) -32982903*a(n-34) -38437964*a(n-35) +11773993*a(n-36) +13043088*a(n-37) -1802183*a(n-38) -2623888*a(n-39) -627392*a(n-40) +445160*a(n-41) +293800*a(n-42) -44672*a(n-43) -29568*a(n-44) for n>46

Example

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

Crossrefs

Cf. A299689.

Sequence in context: A041469 A089102 A098912 * A363449 A268225 A120343

Adjacent sequences: A299682 A299683 A299684 * A299686 A299687 A299688

Keyword

nonn

Author

R. H. Hardin, Feb 16 2018

Status

approved