A305589 Number of nX4 0..1 arrays with every element unequal to 0, 1, 2, 3, 5 or 6 king-move adjacent elements, with upper left element zero.

8, 65, 390, 2451, 14746, 89466, 544280, 3314595, 20186517, 122959746, 749058546, 4563548026, 27804168598, 169406254298, 1032182730787, 6289099847626, 38319805312809, 233485489859306, 1422648513402804, 8668341664825535

Offset

1,1

Comments

Column 4 of A305593.

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) +28*a(n-3) -162*a(n-4) -93*a(n-5) +407*a(n-6) +1195*a(n-7) +1669*a(n-8) -392*a(n-9) -108*a(n-10) -18223*a(n-11) +5342*a(n-12) -22547*a(n-13) -68718*a(n-14) +80676*a(n-15) -115465*a(n-16) +376935*a(n-17) +174298*a(n-18) +382141*a(n-19) -391935*a(n-20) +1058452*a(n-21) -2123771*a(n-22) +2758773*a(n-23) -3785453*a(n-24) -5505707*a(n-25) +8387586*a(n-26) -19508374*a(n-27) +19452792*a(n-28) +3273614*a(n-29) -9839642*a(n-30) -1150520*a(n-31) +15388381*a(n-32) +26576015*a(n-33) -34317006*a(n-34) -15424431*a(n-35) +2695852*a(n-36) -29399288*a(n-37) +11152019*a(n-38) +20424410*a(n-39) -39694874*a(n-40) +78186467*a(n-41) +42408467*a(n-42) -14206230*a(n-43) +814405*a(n-44) +18464832*a(n-45) -21668937*a(n-46) -22553264*a(n-47) +16081493*a(n-48) -26163409*a(n-49) -9663135*a(n-50) +3843853*a(n-51) -87906*a(n-52) +1993634*a(n-53) +345648*a(n-54) -867616*a(n-55) +96128*a(n-56) +200320*a(n-57) for n>59

Example

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

Crossrefs

Cf. A305593.

Sequence in context: A305772 A317121 A009373 * A317007 A293802 A316872

Adjacent sequences: A305586 A305587 A305588 * A305590 A305591 A305592

Keyword

nonn

Author

R. H. Hardin, Jun 05 2018

Status

approved