A300944 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 3, 4 or 6 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

1, 2, 2, 3, 3, 3, 5, 2, 2, 5, 8, 3, 5, 3, 8, 13, 6, 12, 12, 6, 13, 21, 6, 19, 38, 19, 6, 21, 34, 11, 47, 75, 75, 47, 11, 34, 55, 26, 101, 186, 248, 186, 101, 26, 55, 89, 43, 206, 530, 836, 836, 530, 206, 43, 89, 144, 82, 411, 1401, 2975, 3873, 2975, 1401, 411, 82, 144, 233, 178

Offset

1,2

Comments

Table starts

..1..2...3....5.....8.....13......21.......34........55.........89.........144

..2..3...2....3.....6......6......11.......26........43.........82.........178

..3..2...5...12....19.....47.....101......206.......411........882........1851

..5..3..12...38....75....186.....530.....1401......3811......10666.......29764

..8..6..19...75...248....836....2975....10597.....37967.....140091......517221

.13..6..47..186...836...3873...16587....77438....373184....1821648.....8941824

.21.11.101..530..2975..16587...99717...628078...4085574...26803581...176672818

.34.26.206.1401.10597..77438..628078..5562548..48137895..421863566..3738856549

.55.43.411.3811.37967.373184.4085574.48137895.556497081.6615843615.79797690689

Links

R. H. Hardin, Table of n, a(n) for n = 1..220

Formula

Empirical for column k:

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

k=2: a(n) = 2*a(n-1) -a(n-2) +4*a(n-3) -4*a(n-4) +a(n-5) -2*a(n-6) +a(n-7)

k=3: [order 31] for n>32

Example

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

Crossrefs

Column 1 is A000045(n+1).

Column 2 is A300500.

Sequence in context: A275378 A300506 A300888 * A301498 A136132 A136545

Adjacent sequences: A300941 A300942 A300943 * A300945 A300946 A300947

Keyword

nonn,tabl

Author

R. H. Hardin, Mar 16 2018

Status

approved