A279865 Number of n X 1 0..2 arrays with no element unequal to a strict majority of its horizontal and vertical neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

0, 1, 0, 6, 6, 30, 54, 158, 342, 846, 1910, 4446, 10038, 22734, 50838, 113310, 250774, 552654, 1211958, 2647390, 5760630, 12492366, 27003990, 58202526, 125104086, 268228430, 573739254, 1224529758, 2608132022, 5544352206, 11764763670

Offset

1,4

Comments

Column 1 of A279871.

Links

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

Formula

Empirical: a(n) = 3*a(n-1) +3*a(n-2) -11*a(n-3) -6*a(n-4) +12*a(n-5) +8*a(n-6).

Conjectures from Colin Barker, Feb 26 2018: (Start)

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

a(n) = (3*2^n*n^2 + 96*n^2 + 21*2^n*n + 2^(n+4) - 16) / 648 for n even.

a(n) = (3*2^n*n^2 - 96*n^2 + 21*2^n*n + 2^(n+4) + 16) / 648 for n odd.

(End)

Example

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

Crossrefs

Cf. A279871.

Sequence in context: A078637 A147799 A071021 * A321528 A074002 A359741

Adjacent sequences: A279862 A279863 A279864 * A279866 A279867 A279868

Keyword

nonn

Author

R. H. Hardin, Dec 21 2016

Status

approved