A279978 - OEIS

A279978

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

%I #7 Feb 12 2019 12:16:05

%S 0,3,9,24,62,134,277,542,1035,1930,3546,6432,11555,20590,36445,64140,

%T 112326,195866,340241,589038,1016671,1749950,3004610,5147092,8798911,

%U 15012766,25569393,43477440,73814414,125140142,211870477,358260350

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

%H R. H. Hardin, <a href="/A279978/b279978.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 5*a(n-1) - 7*a(n-2) - 2*a(n-3) + 10*a(n-4) - 2*a(n-5) - 5*a(n-6) + a(n-7) + a(n-8) for n>10.

%F Empirical g.f.: x^2*(3 - 6*x + 11*x^3 - 20*x^4 + 5*x^5 + 12*x^6 + 2*x^7 - 5*x^8) / ((1 - x)^2*(1 - x - x^2)^3). - _Colin Barker_, Feb 12 2019

%e Some solutions for n=4:

%e ..0..1..1..0. .0..1..0..1. .0..0..1..0. .0..1..1..0. .0..1..0..0

%e ..0..1..1..0. .0..1..1..1. .1..1..1..0. .0..0..0..1. .1..1..1..0

%Y Row 2 of A279977.

%K nonn

%O 1,2

%A _R. H. Hardin_, Dec 24 2016