A269822 Number of n X 1 0..4 arrays with some element plus some horizontally, diagonally, antidiagonally or vertically adjacent neighbor totalling four exactly once.

0, 5, 40, 240, 1280, 6400, 30720, 143360, 655360, 2949120, 13107200, 57671680, 251658240, 1090519040, 4697620480, 20132659200, 85899345920, 365072220160, 1546188226560, 6528350289920, 27487790694400, 115448720916480

Offset

1,2

Comments

Column 1 of A269829.

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

Empirical: a(n) = 8*a(n-1) - 16*a(n-2).

Conjectures from Colin Barker, Mar 22 2018: (Start)

G.f.: 5*x^2 / (1 - 4*x)^2.

a(n) = 5*4^(n-2)*(n-1).

(End)

Example

Some solutions for n=4:
..1. .2. .2. .4. .4. .3. .2. .4. .4. .0. .0. .0. .2. .3. .3. .2
..1. .3. .3. .2. .3. .4. .2. .4. .0. .1. .0. .3. .3. .0. .1. .4
..1. .1. .2. .4. .1. .1. .3. .3. .0. .4. .4. .4. .4. .1. .0. .0
..3. .0. .2. .0. .0. .3. .3. .1. .3. .0. .1. .0. .0. .3. .3. .3

Crossrefs

Cf. A269829.

Sequence in context: A081364 A261739 A230744 * A043019 A054604 A157794

Adjacent sequences: A269819 A269820 A269821 * A269823 A269824 A269825

Keyword

nonn

Author

R. H. Hardin, Mar 05 2016

Status

approved