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

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Last modified September 24 23:43 EDT 2022. Contains 356951 sequences. (Running on oeis4.)