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.

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

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