A269895 Number of n X 1 0..6 arrays with some element plus some horizontally or vertically adjacent neighbor totalling six exactly once.

0, 7, 84, 756, 6048, 45360, 326592, 2286144, 15676416, 105815808, 705438720, 4655895552, 30474952704, 198087192576, 1279948013568, 8228237230080, 52660718272512, 335712078987264, 2132759090036736, 13507474236899328

Offset

1,2

Comments

Column 1 of A269902.

Links

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

Formula

Empirical: a(n) = 12*a(n-1) - 36*a(n-2).

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

G.f.: 7*x^2 / (1 - 6*x)^2.

a(n) = 7*6^(n-2)*(n-1).

(End)

Example

Some solutions for n=4:
..4. .0. .0. .3. .4. .3. .4. .0. .4. .1. .4. .2. .2. .4. .4. .1
..2. .1. .4. .3. .6. .3. .2. .4. .2. .5. .1. .6. .1. .5. .2. .4
..5. .5. .2. .1. .0. .0. .6. .2. .0. .4. .5. .2. .6. .1. .1. .2
..6. .5. .2. .1. .0. .4. .6. .5. .1. .4. .0. .4. .0. .2. .4. .6

Crossrefs

Cf. A269902.

Sequence in context: A316377 A053128 A027819 * A272496 A177009 A099674

Adjacent sequences: A269892 A269893 A269894 * A269896 A269897 A269898

Keyword

nonn

Author

R. H. Hardin, Mar 07 2016

Status

approved