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A299314
T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 4, 5, 6 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, 29, 29, 23, 5, 8, 49, 63, 112, 63, 49, 8, 13, 99, 199, 504, 504, 199, 99, 13, 21, 189, 593, 2528, 3463, 2528, 593, 189, 21, 34, 383, 1657, 11252, 24519, 24519, 11252, 1657, 383, 34, 55, 777, 4689, 50720, 167810
OFFSET
1,5
COMMENTS
Table starts
..0...1....1......2.......3.........5...........8...........13.............21
..1...3....7.....13......23........49..........99..........189............383
..1...7...15.....29......63.......199.........593.........1657...........4689
..2..13...29....112.....504......2528.......11252........50720.........241309
..3..23...63....504....3463.....24519......167810......1165033........8305148
..5..49..199...2528...24519....270346.....3203795.....36378590......417642077
..8..99..593..11252..167810...3203795....60731972...1089584523....20249517439
.13.189.1657..50720.1165033..36378590..1089584523..30975700202...924197633148
.21.383.4689.241309.8305148.417642077.20249517439.924197633148.44405195921475
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 16] for n>17
k=4: [order 62] for n>66
EXAMPLE
Some solutions for n=5 k=4
..0..1..0..0. .0..0..1..0. .0..1..1..0. .0..0..0..0. .0..1..1..0
..0..1..1..1. .1..1..1..0. .0..0..0..1. .1..0..0..1. .0..0..1..0
..0..1..1..0. .0..0..1..1. .0..0..0..1. .0..1..0..1. .0..0..1..1
..0..1..1..0. .1..0..1..1. .1..0..0..1. .1..0..0..1. .0..0..1..1
..0..1..0..1. .0..1..0..1. .0..1..0..1. .1..0..1..0. .0..1..0..1
CROSSREFS
Column 1 is A000045(n-1).
Column 2 is A297953.
Sequence in context: A299574 A298396 A299514 * A300115 A100888 A322469
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Feb 06 2018
STATUS
approved