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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. 7
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified September 16 10:46 EDT 2019. Contains 327094 sequences. (Running on oeis4.)