A299521 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 3, 4, 5, 6 or 8 king-move adjacent elements, with upper left element zero.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 12, 2, 1, 1, 5, 5, 5, 5, 1, 1, 9, 33, 8, 33, 9, 1, 1, 22, 55, 41, 41, 55, 22, 1, 1, 45, 132, 117, 285, 117, 132, 45, 1, 1, 101, 272, 476, 1540, 1540, 476, 272, 101, 1, 1, 218, 630, 1743, 5869, 12411, 5869, 1743, 630, 218, 1, 1, 477, 1355, 7078

Offset

1,12

Comments

Table starts

.1...1...1....1......1.......1.........1..........1............1.............1

.1...1...1....2......5.......9........22.........45..........101...........218

.1...1..12....5.....33......55.......132........272..........630..........1355

.1...2...5....8.....41.....117.......476.......1743.........7078.........28743

.1...5..33...41....285....1540......5869......31464.......164344........875093

.1...9..55..117...1540...12411.....89125.....826509......7492106......69199615

.1..22.132..476...5869...89125....902141...12982595....174024827....2513147146

.1..45.272.1743..31464..826509..12982595..310347496...6868847887..161346598727

.1.101.630.7078.164344.7492106.174024827.6868847887.249358437986.9535286392860

Links

R. H. Hardin, Table of n, a(n) for n = 1..197

Formula

Empirical for column k:

k=1: a(n) = a(n-1)

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

k=3: [order 12] for n>13

k=4: [order 34] for n>36

Example

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

Crossrefs

Column 2 is A052962(n-2).

Sequence in context: A211798 A075180 A227830 * A167164 A277265 A263631

Adjacent sequences: A299518 A299519 A299520 * A299522 A299523 A299524

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 11 2018

Status

approved