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A299514 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 4, 5, 6 or 8 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, 167, 439, 439, 167, 99, 13, 21, 189, 477, 1950, 2336, 1950, 477, 189, 21, 34, 383, 1233, 7702, 13836, 13836, 7702, 1233, 383, 34, 55, 777, 3265, 30277, 84449, 122197 (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......167........477........1233..........3265

..2..13...29....112.....439.....1950.......7702.......30277........126429

..3..23...63....439....2336....13836......84449......477162.......2791607

..5..49..167...1950...13836...122197....1190886....10305454......92938855

..8..99..477...7702...84449..1190886...17345466...225351737....3159884395

.13.189.1233..30277..477162.10305454..225351737..4446967161...94825218644

.21.383.3265.126429.2791607.92938855.3159884395.94825218644.3109567007082

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 15] for n>17

k=4: [order 68] for n>70

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..1

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

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

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

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

CROSSREFS

Column 1 is A000045(n-1).

Column 2 is A297953.

Sequence in context: A298582 A299574 A298396 * A299314 A300115 A100888

Adjacent sequences: A299511 A299512 A299513 * A299515 A299516 A299517

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Feb 11 2018

STATUS

approved

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Last modified February 6 11:02 EST 2023. Contains 360104 sequences. (Running on oeis4.)