A298582 - OEIS

A298582

T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 4, 5 or 7 king-move adjacent elements, with upper left element zero.

0, 1, 1, 1, 3, 1, 2, 7, 7, 2, 3, 13, 15, 13, 3, 5, 23, 25, 25, 23, 5, 8, 49, 47, 78, 47, 49, 8, 13, 99, 113, 237, 237, 113, 99, 13, 21, 189, 261, 844, 765, 844, 261, 189, 21, 34, 383, 601, 2551, 3284, 3284, 2551, 601, 383, 34, 55, 777, 1397, 7941, 14482, 16521, 14482, 7941

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OFFSET

1,5

COMMENTS

Table starts

..0...1....1.....2......3.......5........8........13.........21..........34

..1...3....7....13.....23......49.......99.......189........383.........777

..1...7...15....25.....47.....113......261.......601.......1397........3223

..2..13...25....78....237.....844.....2551......7941......25802.......82080

..3..23...47...237....765....3284....14482.....53272.....215514......912084

..5..49..113...844...3284...16521....90381....457878....2383346....12834179

..8..99..261..2551..14482...90381...708805...4703257...33115108...242951715

.13.189..601..7941..53272..457878..4703257..40964223..383092595..3711048926

.21.383.1397.25802.215514.2383346.33115108.383092595.4776371282.61947087103

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..199

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) for n>5

k=3: [order 14] for n>15

k=4: [order 68] for n>69

EXAMPLE

Some solutions for n=5 k=4

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

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

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

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

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

CROSSREFS

Column 1 is A000045(n-1).

Column 2 is A297953.

Sequence in context: A299612 A297959 A298775 * A299574 A298396 A299514

Adjacent sequences: A298579 A298580 A298581 * A298583 A298584 A298585

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Jan 22 2018

STATUS

approved