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.

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

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