A316872 Number of nX4 0..1 arrays with every element unequal to 0, 1, 2, 3, 5, 6 or 7 king-move adjacent elements, with upper left element zero.

8, 65, 425, 2931, 19363, 129974, 871345, 5848852, 39278049, 263713497, 1770482001, 11887215402, 79812178186, 535861305908, 3597799009537, 24155860662607, 162183882073432, 1088911875204984, 7311018935280645, 49086615774849387

Offset

1,1

Comments

Column 4 of A316876.

Links

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

Formula

Empirical: a(n) = 9*a(n-1) -18*a(n-2) +56*a(n-3) -259*a(n-4) -64*a(n-5) +211*a(n-6) +1886*a(n-7) +2523*a(n-8) +878*a(n-9) -9154*a(n-10) -13683*a(n-11) +6221*a(n-12) -38007*a(n-13) +8906*a(n-14) -128091*a(n-15) -107882*a(n-16) +315762*a(n-17) +363860*a(n-18) +1101826*a(n-19) +846143*a(n-20) +427920*a(n-21) -2427427*a(n-22) +3511785*a(n-23) -2728517*a(n-24) +2625660*a(n-25) -5151730*a(n-26) -11861440*a(n-27) -8821843*a(n-28) -21636271*a(n-29) +13157246*a(n-30) -59443053*a(n-31) -22854215*a(n-32) -11238396*a(n-33) -14226060*a(n-34) +9927279*a(n-35) -11806156*a(n-36) +52958705*a(n-37) -10385036*a(n-38) +95481445*a(n-39) +42796528*a(n-40) +3577309*a(n-41) +61364104*a(n-42) +4763501*a(n-43) +9804404*a(n-44) +279972*a(n-45) -7073065*a(n-46) -9689912*a(n-47) -253349*a(n-48) -4170945*a(n-49) -5659326*a(n-50) -711496*a(n-51) +1217130*a(n-52) +1142541*a(n-53) -350714*a(n-54) -395908*a(n-55) -50160*a(n-56) for n>58

Example

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

Crossrefs

Cf. A316876.

Sequence in context: A305589 A317007 A293802 * A317600 A288788 A033118

Adjacent sequences: A316869 A316870 A316871 * A316873 A316874 A316875

Keyword

nonn

Author

R. H. Hardin, Jul 15 2018

Status

approved