A318430 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 3 or 6 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

0, 1, 1, 1, 5, 1, 2, 16, 16, 2, 3, 50, 36, 50, 3, 5, 160, 147, 147, 160, 5, 8, 511, 417, 889, 417, 511, 8, 13, 1634, 1353, 3999, 3999, 1353, 1634, 13, 21, 5226, 4095, 20016, 19645, 20016, 4095, 5226, 21, 34, 16716, 12853, 95349, 132039, 132039, 95349, 12853, 16716

Offset

1,5

Comments

Table starts

..0.....1.....1.......2........3.........5...........8...........13

..1.....5....16......50......160.......511........1634.........5226

..1....16....36.....147......417......1353........4095........12853

..2....50...147.....889.....3999.....20016.......95349.......461349

..3...160...417....3999....19645....132039......774731......4831925

..5...511..1353...20016...132039...1216538.....9600648.....81327718

..8..1634..4095...95349...774731...9600648....99435165...1103814944

.13..5226.12853..461349..4831925..81327718..1103814944..16560787736

.21.16716.39489.2221254.29346956.665822482.11993654843.238281611555

Links

R. H. Hardin, Table of n, a(n) for n = 1..263

Formula

Empirical for column k:

k=1: a(n) = a(n-1) +a(n-2)

k=2: a(n) = 3*a(n-1) +a(n-2) -3*a(n-4) -2*a(n-5) -a(n-6)

k=3: [order 17] for n>20

k=4: [order 53] for n>59

Example

Some solutions for n=5 k=4
..0..1..1..0. .0..1..1..1. .0..1..1..0. .0..1..1..0. .0..1..1..1
..0..1..1..0. .0..0..0..1. .0..1..1..1. .1..1..0..1. .1..0..0..1
..0..1..1..0. .1..0..0..1. .0..0..0..0. .0..0..0..1. .0..0..0..1
..1..0..1..1. .1..0..0..0. .0..0..0..1. .1..0..0..0. .0..1..0..1
..1..1..1..0. .0..1..1..1. .1..0..1..0. .1..1..1..0. .0..0..0..0

Crossrefs

Column 1 is A000045(n-1).

Column 2 is A317817.

Sequence in context: A258339 A197080 A317823 * A318098 A318068 A165449

Adjacent sequences: A318427 A318428 A318429 * A318431 A318432 A318433

Keyword

nonn,tabl

Author

R. H. Hardin, Aug 26 2018

Status

approved