A268900 Number of n X 4 0..2 arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling two exactly once.

36, 696, 9720, 118584, 1347192, 14644152, 154472184, 1594323000, 16185567096, 162200044728, 1608569870328, 15816054042936, 154394813276280, 1498006261495224, 14458132831535352, 138907883786523192

Offset

1,1

Links

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

Formula

Empirical: a(n) = 18*a(n-1) - 81*a(n-2) for n>3.

Conjectures from Colin Barker, Jan 16 2019: (Start)

G.f.: 12*x*(3 + 4*x + 9*x^2) / (1 - 9*x)^2.

a(n) = 8 * 3^(2*n-3) * (16*n-3) for n>1.

(End)

Example

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

Crossrefs

Column 4 of A268904.

Sequence in context: A053947 A157092 A004419 * A185491 A220758 A054339

Adjacent sequences: A268897 A268898 A268899 * A268901 A268902 A268903

Keyword

nonn

Author

R. H. Hardin, Feb 15 2016

Status

approved