A316583 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 3, 4, 7 or 8 king-move adjacent elements, with upper left element zero.

0, 1, 1, 1, 7, 1, 2, 23, 23, 2, 3, 86, 63, 86, 3, 5, 313, 338, 338, 313, 5, 8, 1145, 1312, 2477, 1312, 1145, 8, 13, 4184, 5936, 15200, 15200, 5936, 4184, 13, 21, 15293, 25271, 98828, 130212, 98828, 25271, 15293, 21, 34, 55895, 110555, 634867, 1216428, 1216428

Offset

1,5

Comments

Table starts

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

..1.....7.....23.......86.......313........1145..........4184..........15293

..1....23.....63......338......1312........5936.........25271.........110555

..2....86....338.....2477.....15200.......98828........634867........4075278

..3...313...1312....15200....130212.....1216428......11450072......105422515

..5..1145...5936....98828...1216428....15492767.....209344758.....2702476568

..8..4184..25271...634867..11450072...209344758....4227286531....79708721021

.13.15293.110555..4075278.105422515..2702476568...79708721021..2151886485463

.21.55895.478290.26237510.988545949.35886237100.1560689236544.60957630655386

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) +a(n-2)

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

k=3: [order 15] for n>16

k=4: [order 46] for n>48

Example

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

Crossrefs

Column 1 is A000045(n-1).

Column 2 is A303890.

Sequence in context: A303896 A305288 A304901 * A304597 A316383 A306143

Adjacent sequences: A316580 A316581 A316582 * A316584 A316585 A316586

Keyword

nonn,tabl

Author

R. H. Hardin, Jul 07 2018

Status

approved