A316757 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 4, 6, 7 or 8 king-move adjacent elements, with upper left element zero.

0, 1, 1, 1, 3, 1, 2, 9, 9, 2, 3, 10, 15, 10, 3, 5, 27, 17, 17, 27, 5, 8, 109, 79, 20, 79, 109, 8, 13, 168, 185, 37, 37, 185, 168, 13, 21, 349, 315, 142, 642, 142, 315, 349, 21, 34, 1229, 970, 295, 3366, 3366, 295, 970, 1229, 34, 55, 2490, 2366, 467, 4397, 10850, 4397, 467

Offset

1,5

Comments

Table starts

..0....1....1....2......3......5.......8.......13........21.........34

..1....3....9...10.....27....109.....168......349......1229.......2490

..1....9...15...17.....79....185.....315......970......2366.......4927

..2...10...17...20.....37....142.....295......467......1217.......3160

..3...27...79...37....642...3366....4397....25154....137845.....309382

..5..109..185..142...3366..10850...23857...205529....822953....2592451

..8..168..315..295...4397..23857...58615...399831...2330661....8452508

.13..349..970..467..25154.205529..399831..6782306..59924254..227254610

.21.1229.2366.1217.137845.822953.2330661.59924254.484120209.2493080136

Links

R. H. Hardin, Table of n, a(n) for n = 1..220

Formula

Empirical for column k:

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

k=2: a(n) = a(n-1) +a(n-2) +8*a(n-3) -16*a(n-5) for n>6

k=3: [order 16] for n>17

k=4: [order 71] for n>72

Example

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

Crossrefs

Column 1 is A000045(n-1).

Column 2 is A305091.

Sequence in context: A378813 A132323 A305097 * A055450 A185835 A301669

Adjacent sequences: A316754 A316755 A316756 * A316758 A316759 A316760

Keyword

nonn,tabl

Author

R. H. Hardin, Jul 12 2018

Status

approved