A317000 Number of nX4 0..1 arrays with every element unequal to 0, 1, 2, 3, 4, 6 or 8 king-move adjacent elements, with upper left element zero.

8, 112, 894, 7665, 65047, 551591, 4691054, 39872525, 338839996, 2880214407, 24480775050, 208076532466, 1768595321211, 15032497751286, 127771476379352, 1086018367787700, 9230818232111217, 78459088020437037, 666877926678011124

Offset

1,1

Comments

Column 4 of A317004.

Links

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

Formula

Empirical: a(n) = 9*a(n-1) -2*a(n-2) +25*a(n-3) -425*a(n-4) +367*a(n-5) +403*a(n-6) +473*a(n-7) +1648*a(n-8) -3461*a(n-9) +6164*a(n-10) -9256*a(n-11) +2080*a(n-12) -13635*a(n-13) +8004*a(n-14) +35269*a(n-15) -49801*a(n-16) +87317*a(n-17) -234670*a(n-18) +108336*a(n-19) +14477*a(n-20) -250949*a(n-21) +582289*a(n-22) -389235*a(n-23) -64042*a(n-24) -159517*a(n-25) -284843*a(n-26) +237493*a(n-27) -125168*a(n-28) +157711*a(n-29) -29761*a(n-30) +34000*a(n-31) +3534*a(n-32) +19585*a(n-33) +5417*a(n-34) +2860*a(n-35) +689*a(n-36) -6*a(n-37) +54*a(n-38) for n>39

Example

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

Crossrefs

Cf. A317004.

Sequence in context: A305765 A317114 A305526 * A316818 A317568 A075851

Adjacent sequences: A316997 A316998 A316999 * A317001 A317002 A317003

Keyword

nonn

Author

R. H. Hardin, Jul 18 2018

Status

approved