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A299465 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 3, 5, 6 or 8 king-move adjacent elements, with upper left element zero. 7
0, 1, 1, 1, 4, 1, 2, 18, 18, 2, 3, 52, 57, 52, 3, 5, 174, 226, 226, 174, 5, 8, 604, 861, 1013, 861, 604, 8, 13, 2048, 3432, 5294, 5294, 3432, 2048, 13, 21, 6948, 13268, 27639, 52002, 27639, 13268, 6948, 21, 34, 23652, 51790, 139226, 402789, 402789, 139226, 51790 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

Table starts

..0.....1......1.......2.........3..........5............8............13

..1.....4.....18......52.......174........604.........2048..........6948

..1....18.....57.....226.......861.......3432........13268.........51790

..2....52....226....1013......5294......27639.......139226........713421

..3...174....861....5294.....52002.....402789......2991315......25096585

..5...604...3432...27639....402789....4175049.....41279802.....478753977

..8..2048..13268..139226...2991315...41279802....546467591....8711452672

.13..6948..51790..713421..25096585..478753977...8711452672..209501211322

.21.23652.202533.3674765.203284013.5290010417.130278485534.4519722020986

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) = 4*a(n-1) -2*a(n-2) +2*a(n-3) -6*a(n-4) -4*a(n-5) for n>6

k=3: [order 20] for n>21

k=4: [order 69] for n>71

EXAMPLE

Some solutions for n=5 k=6

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

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

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

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

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

CROSSREFS

Column 1 is A000045(n-1).

Column 2 is A297945.

Sequence in context: A299307 A298770 A299567 * A300108 A298280 A299142

Adjacent sequences: A299462 A299463 A299464 * A299466 A299467 A299468

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Feb 10 2018

STATUS

approved

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Last modified December 8 14:17 EST 2022. Contains 358693 sequences. (Running on oeis4.)