A299728 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 3, 4, 5, 6 or 7 king-move adjacent elements, with upper left element zero.

0, 1, 1, 1, 4, 1, 2, 18, 18, 2, 3, 64, 141, 64, 3, 5, 236, 1027, 1027, 236, 5, 8, 888, 7664, 14701, 7664, 888, 8, 13, 3336, 57471, 217069, 217069, 57471, 3336, 13, 21, 12512, 430401, 3224826, 6354153, 3224826, 430401, 12512, 21, 34, 46928, 3222716

Offset

1,5

Comments

Table starts

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

..1.....4......18........64..........236............888.............3336

..1....18.....141......1027.........7664..........57471...........430401

..2....64....1027.....14701.......217069........3224826.........47845523

..3...236....7664....217069......6354153......187530622.......5526277711

..5...888...57471...3224826....187530622....10997877289.....643936117646

..8..3336..430401..47845523...5526277711...643936117646...74902586591536

.13.12512.3222716.709688988.162794536467.37689687396652.8709586033088978

Links

R. H. Hardin, Table of n, a(n) for n = 1..264

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) +4*a(n-3) for n>4

k=3: a(n) = 6*a(n-1) +8*a(n-2) +20*a(n-3) +25*a(n-4) +11*a(n-5) +2*a(n-6) for n>7

k=4: [order 16] for n>17

k=5: [order 39] for n>40

k=6: [order 92] for n>93

Example

Some solutions for n=5 k=4
..0..0..0..1. .0..0..0..1. .0..0..0..0. .0..0..0..1. .0..0..0..0
..1..0..0..1. .0..0..0..1. .1..0..1..0. .0..1..1..1. .1..0..1..0
..1..0..1..0. .0..1..0..0. .1..0..1..1. .1..0..1..0. .1..0..1..1
..0..0..1..1. .0..1..1..0. .0..1..0..1. .1..1..1..0. .1..0..1..1
..1..1..0..1. .0..1..0..0. .1..1..0..0. .1..0..0..0. .1..1..0..0

Crossrefs

Column 1 is A000045(n-1).

Column 2 is A231950(n-1).

Sequence in context: A299373 A299937 A299067 * A299839 A265178 A159766

Adjacent sequences: A299725 A299726 A299727 * A299729 A299730 A299731

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 17 2018

Status

approved