A305685 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 2, 3, 4, 5 or 6 king-move adjacent elements, with upper left element zero.

1, 1, 1, 1, 4, 1, 1, 8, 8, 1, 1, 24, 25, 24, 1, 1, 82, 139, 139, 82, 1, 1, 272, 818, 1595, 818, 272, 1, 1, 908, 4869, 17947, 17947, 4869, 908, 1, 1, 3076, 29339, 207116, 383910, 207116, 29339, 3076, 1, 1, 10444, 177688, 2403703, 8417922, 8417922, 2403703

Offset

1,5

Comments

Table starts

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

.1.....4.......8........24..........82............272..............908

.1.....8......25.......139.........818...........4869............29339

.1....24.....139......1595.......17947.........207116..........2403703

.1....82.....818.....17947......383910........8417922........185389115

.1...272....4869....207116.....8417922......351440611......14724197226

.1...908...29339...2403703...185389115....14724197226....1172824606532

.1..3076..177688..27979008..4094434997...618597002816...93679147557172

.1.10444.1078090.325990496.90512430926.26011056462909.7488807032051960

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)

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 14] for n>16

k=4: [order 38] for n>40

Example

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

Crossrefs

Column 2 is A303882.

Sequence in context: A316244 A305954 A317215 * A317065 A316932 A317703

Adjacent sequences: A305682 A305683 A305684 * A305686 A305687 A305688

Keyword

nonn,tabl

Author

R. H. Hardin, Jun 08 2018

Status

approved