A317065 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 2, 3, 4, 5, 6 or 8 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, 384535, 207116, 29339, 3076, 1, 1, 10444, 177688, 2403703, 8450612, 8450612, 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......384535........8450612........186574154

.1...272....4869....207116.....8450612......354399907......14920072888

.1...908...29339...2403703...186574154....14920072888....1197129513001

.1..3076..177688..27979008..4130997988...629855730272...96317261216226

.1.10444.1078090.325990496.91552460948.26612973830635.7756014658872472

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..1..0. .0..0..1..1. .0..1..1..1
..1..1..0..1. .1..0..0..0. .0..1..1..0. .1..1..0..0. .1..1..0..0
..1..0..0..1. .0..0..0..1. .1..1..0..1. .0..0..1..0. .1..0..0..1
..1..0..0..1. .1..1..1..0. .0..0..0..0. .1..1..1..1. .0..1..1..0
..0..1..0..1. .0..1..0..1. .1..0..1..1. .0..0..1..0. .0..1..0..1

Crossrefs

Column 2 is A303882.

Column 3 is A305680.

Column 4 is A305681.

Sequence in context: A305954 A317215 A305685 * A316932 A317703 A055107

Adjacent sequences: A317062 A317063 A317064 * A317066 A317067 A317068

Keyword

nonn,tabl

Author

R. H. Hardin, Jul 20 2018

Status

approved