A269215 Number of 2 X n 0..3 arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling three exactly once.

0, 96, 768, 6528, 49536, 360960, 2546304, 17563392, 119091072, 796813824, 5274483840, 34608512256, 225420724608, 1459142258688, 9394561013376, 60205610853120, 384263133750144, 2443755614295552, 15491594556534912

Offset

1,2

Comments

Row 2 of A269214.

Links

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

Formula

Empirical: a(n) = 10*a(n-1) - 13*a(n-2) - 60*a(n-3) - 36*a(n-4).

From Colin Barker, Mar 21 2018: (Start)

G.f.: 96*x^2*(1 - x)^2 / ((1 + x)^2*(1 - 6*x)^2).

a(n) = 8*(175*6^n*n + 1008*n - 55*6^n - 288) / 1029 for n even.

a(n) = 8*(175*6^n*n - 1008*n - 55*6^n + 288) / 1029 for n odd.

(End)

Example

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

Crossrefs

Cf. A269214.

Sequence in context: A232405 A269032 A187610 * A096783 A253410 A326576

Adjacent sequences: A269212 A269213 A269214 * A269216 A269217 A269218

Keyword

nonn

Author

R. H. Hardin, Feb 20 2016

Status

approved