A269760 Number of n X 1 0..5 arrays with some element plus some horizontally or vertically adjacent neighbor totalling five exactly once.

0, 6, 60, 450, 3000, 18750, 112500, 656250, 3750000, 21093750, 117187500, 644531250, 3515625000, 19042968750, 102539062500, 549316406250, 2929687500000, 15563964843750, 82397460937500, 434875488281250

Offset

1,2

Comments

Column 1 of A269767.

Links

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

Formula

Empirical: a(n) = 10*a(n-1) - 25*a(n-2).

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

G.f.: 6*x^2 / (1 - 5*x)^2.

a(n) = 6*5^(n-2)*(n-1).

(End)

Example

Some solutions for n=4:
..0. .2. .4. .2. .2. .5. .1. .0. .3. .1. .1. .5. .5. .2. .4. .0
..5. .3. .1. .5. .0. .1. .0. .4. .1. .1. .5. .0. .3. .4. .5. .0
..2. .3. .3. .0. .2. .4. .5. .2. .3. .4. .0. .3. .4. .1. .1. .5
..1. .0. .5. .0. .3. .5. .4. .3. .2. .0. .2. .3. .1. .1. .4. .3

Crossrefs

Cf. A269767.

Sequence in context: A000911 A076100 A353040 * A043033 A179711 A061495

Adjacent sequences: A269757 A269758 A269759 * A269761 A269762 A269763

Keyword

nonn

Author

R. H. Hardin, Mar 04 2016

Status

approved