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

1,5

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

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) = 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

Example

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

Crossrefs

Column 2 is A180762.

Row 1 is A000045(n-1).

Row 2 is A302225.

Row 3 is A302226.

Row 4 is A302227.

Sequence in context: A239098 A319501 A302224 * A302472 A303254 A256068

Adjacent sequences: A302667 A302668 A302669 * A302671 A302672 A302673

Keyword

nonn,tabl

Author

R. H. Hardin, Apr 11 2018

Status

approved