A270111 Number of n X 1 0..7 arrays with some element plus some horizontally or vertically adjacent neighbor totalling seven exactly once.

0, 8, 112, 1176, 10976, 96040, 806736, 6588344, 52706752, 415065672, 3228288560, 24857821912, 189823367328, 1439493868904, 10851569165584, 81386768741880, 607687873272704, 4519678557465736, 33498794014157808, 247518866882388248

Offset

1,2

Comments

Column 1 of A270118.

Links

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

Formula

Empirical: a(n) = 14*a(n-1) - 49*a(n-2).

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

G.f.: 8*x^2 / (1 - 7*x)^2.

a(n) = 8*7^(n-2)*(n-1).

(End)

Example

Some solutions for n=4:
..5. .5. .6. .5. .0. .4. .7. .4. .4. .5. .7. .0. .7. .7. .1. .5
..6. .5. .2. .2. .7. .3. .1. .3. .5. .2. .1. .4. .6. .2. .3. .0
..7. .2. .2. .2. .1. .3. .6. .1. .3. .4. .6. .3. .1. .6. .4. .7
..0. .3. .5. .3. .2. .6. .6. .5. .4. .0. .7. .6. .7. .1. .5. .7

Crossrefs

Cf. A270118.

Sequence in context: A316818 A317568 A075851 * A053536 A139741 A067900

Adjacent sequences: A270108 A270109 A270110 * A270112 A270113 A270114

Keyword

nonn

Author

R. H. Hardin, Mar 11 2016

Status

approved