A280399 Number of 1 X n 0..2 arrays with no element unequal to a strict majority of its horizontal and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

0, 0, 2, 2, 8, 14, 36, 74, 168, 358, 780, 1666, 3568, 7582, 16084, 33978, 71608, 150486, 315548, 660210, 1378688, 2873870, 5980772, 12427562, 25787208, 53438534, 110605356, 228667234, 472247568, 974321278, 2008294900, 4135894426

Offset

1,3

Links

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

Formula

Empirical: a(n) = 2*a(n-1) + 3*a(n-2) - 4*a(n-3) - 4*a(n-4) for n>5.

Conjectures from Colin Barker, Feb 13 2019: (Start)

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

a(n) = (8*((-1)^(1+n)+2^n) + 3*(-8*(-1)^n+2^n)*n) / 108 for n>1.

(End)

Example

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

Crossrefs

Row 1 of A280398.

Sequence in context: A357787 A045686 A045677 * A005633 A228661 A369316

Adjacent sequences: A280396 A280397 A280398 * A280400 A280401 A280402

Keyword

nonn

Author

R. H. Hardin, Jan 02 2017

Status

approved