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A300546 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 3 or 4 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero. 7
0, 1, 1, 1, 3, 1, 2, 11, 11, 2, 3, 37, 71, 37, 3, 5, 129, 450, 450, 129, 5, 8, 450, 2879, 5232, 2879, 450, 8, 13, 1568, 18365, 61561, 61561, 18365, 1568, 13, 21, 5464, 117146, 724165, 1338834, 724165, 117146, 5464, 21, 34, 19041, 747252, 8514930, 29114990 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

Table starts

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

..1.....3......11.........37..........129............450..............1568

..1....11......71........450.........2879..........18365............117146

..2....37.....450.......5232........61561.........724165...........8514930

..3...129....2879......61561......1338834.......29114990.........632777378

..5...450...18365.....724165.....29114990.....1170734982.......47042626155

..8..1568..117146....8514930....632777378....47042626155.....3494400946777

.13..5464..747252..100122064..13752553340..1890308500802...259582877324570

.21.19041.4766519.1177281510.298894998879.75958861124241.19283328543117575

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..219

FORMULA

Empirical for column k:

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

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

k=3: [order 8] for n>10

k=4: [order 41] for n>42

EXAMPLE

Some solutions for n=5 k=4

..0..1..1..1. .0..1..1..0. .0..0..1..0. .0..0..1..0. .0..0..0..1

..0..1..0..0. .0..1..1..0. .0..1..0..1. .1..1..0..1. .1..1..0..1

..1..1..0..1. .1..0..0..0. .1..0..1..0. .0..1..1..1. .1..0..1..1

..0..0..1..1. .0..1..0..0. .0..1..0..1. .0..0..0..0. .0..0..0..1

..0..0..1..1. .0..1..1..0. .0..1..1..1. .1..1..1..1. .1..1..0..0

CROSSREFS

Column 1 is A000045(n-1).

Column 2 is A232031(n-1).

Sequence in context: A317458 A301615 A180771 * A300973 A300930 A109528

Adjacent sequences:  A300543 A300544 A300545 * A300547 A300548 A300549

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Mar 08 2018

STATUS

approved

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Last modified October 23 21:27 EDT 2021. Contains 348217 sequences. (Running on oeis4.)