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

R. H. Hardin, Table of n, a(n) for n = 1..180

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

Adjacent sequences:  A299311 A299312 A299313 * A299315 A299316 A299317

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Feb 06 2018

STATUS

approved

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Last modified July 6 02:58 EDT 2022. Contains 355108 sequences. (Running on oeis4.)