A300546 - OEIS

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.

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

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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