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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
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
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
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Jan 22 2018
STATUS
approved