A302670 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 3 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

0, 1, 0, 1, 3, 0, 2, 14, 11, 0, 3, 45, 43, 34, 0, 5, 146, 164, 194, 111, 0, 8, 537, 760, 934, 691, 361, 0, 13, 1934, 3425, 6110, 4267, 2802, 1172, 0, 21, 6861, 15569, 38736, 42367, 21949, 10660, 3809, 0, 34, 24386, 70323, 251254, 352174, 316977, 106793, 41839

Offset: 1

Author

R. H. Hardin, Apr 11 2018

Keywords

• nonn
• tabl

Comments

Table starts

.0.....1......1.......2.........3..........5............8............13

.0.....3.....14......45.......146........537.........1934..........6861

.0....11.....43.....164.......760.......3425........15569.........70323

.0....34....194.....934......6110......38736.......251254.......1610569

.0...111....691....4267.....42367.....352174......3204956......28324200

.0...361...2802...21949....316977....3640304.....46360666.....582115385

.0..1172..10660..106793...2320879...35549458....637088915...11181864782

.0..3809..41839..529984..17037458..353912413...8880747825..219692176894

.0.12377.161878.2617548.125456575.3503182605.123521424862.4291098950499

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..180

Crossrefs

Column 2 is A180762.

Row 1 is A000045(n-1).

Row 2 is A302225.

Row 3 is A302226.

Row 4 is A302227.

Formula

Empirical for column k:

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

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

k=3: [order 14]

k=4: [order 32] for n>35

Empirical for row n:

n=1: a(n) = a(n-1) +a(n-2)

n=2: a(n) = 2*a(n-1) +3*a(n-2) +6*a(n-3) +10*a(n-4) +4*a(n-5) for n>6

n=3: [order 15] for n>17

n=4: [order 54] for n>58