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A300108 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 3, 5, 6, 7 or 8 king-move adjacent elements, with upper left element zero. 6
0, 1, 1, 1, 4, 1, 2, 18, 18, 2, 3, 52, 57, 52, 3, 5, 174, 226, 226, 174, 5, 8, 604, 861, 1041, 861, 604, 8, 13, 2048, 3432, 5526, 5526, 3432, 2048, 13, 21, 6948, 13268, 29439, 59014, 29439, 13268, 6948, 21, 34, 23652, 51790, 150416, 526613, 526613, 150416, 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....1041......5526.......29439.......150416.........781647

..3...174....861....5526.....59014......526613......4330629.......39686493

..5...604...3432...29439....526613.....7603542.....96369782.....1370857737

..8..2048..13268..150416...4330629....96369782...1781758380....37174337571

.13..6948..51790..781647..39686493..1370857737..37174337571..1206489116900

.21.23652.202533.4082439.361139457.19722172824.798263732216.40745626588281

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 67] for n>69

EXAMPLE

Some solutions for n=5 k=4

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

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

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

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

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

CROSSREFS

Column 1 is A000045(n-1).

Column 2 is A297945.

Column 3 is A299460.

Sequence in context: A298770 A299567 A299465 * A298280 A299142 A299373

Adjacent sequences: A300105 A300106 A300107 * A300109 A300110 A300111

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Feb 25 2018

STATUS

approved

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Last modified December 1 01:13 EST 2022. Contains 358453 sequences. (Running on oeis4.)