A280174 Number of n X 2 0..1 arrays with no element unequal to a strict majority of its horizontal, vertical and antidiagonal neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

1, 2, 12, 41, 103, 263, 656, 1618, 3931, 9459, 22557, 53395, 125594, 293796, 683972, 1585588, 3661900, 8428646, 19341455, 44261305, 101034472, 230100558, 522936849, 1186138105, 2685582035, 6070360107, 13699764020, 30873005212, 69478759648

Offset

1,2

Links

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

Formula

Empirical: a(n) = 4*a(n-1) - 11*a(n-3) - 4*a(n-4) + 15*a(n-5) + 14*a(n-6) - 2*a(n-7) - 9*a(n-8) - 5*a(n-9) - a(n-10) for n>14.

Empirical g.f.: x*(1 - 2*x + 4*x^2 + 4*x^3 - 35*x^4 - 24*x^5 + 59*x^6 + 85*x^7 - 6*x^8 - 69*x^9 - 43*x^10 - 5*x^11 + 3*x^12 + x^13) / ((1 - x)*(1 - x - 2*x^2 - x^3)^3). - Colin Barker, Feb 13 2019

Example

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

Crossrefs

Column 2 of A280180.

Sequence in context: A098519 A127725 A371357 * A185619 A048014 A364598

Adjacent sequences: A280171 A280172 A280173 * A280175 A280176 A280177

Keyword

nonn

Author

R. H. Hardin, Dec 28 2016

Status

approved