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A279972 Number of n X 3 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 A279972 #7 Feb 12 2019 12:02:57
%S A279972 0,9,50,296,1650,8666,43543,211650,1002602,4652327,21225237,95473540,
%T A279972 424318824,1866436977,8136431834,35191126234,151149336828,
%U A279972 645183934470,2738696392197,11567109056460,48632928912442,203627897130121
%N A279972 Number of n X 3 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 A279972 R. H. Hardin, <a href="/A279972/b279972.txt">Table of n, a(n) for n = 1..210</a>
%F A279972 Empirical: a(n) = 15*a(n-1) - 90*a(n-2) + 281*a(n-3) - 510*a(n-4) + 585*a(n-5) - 437*a(n-6) + 210*a(n-7) - 60*a(n-8) + 8*a(n-9) for n>10.
%F A279972 Empirical g.f.: x^2*(9 - 85*x + 356*x^2 - 819*x^3 + 1096*x^4 - 888*x^5 + 438*x^6 - 124*x^7 + 16*x^8) / (1 - 5*x + 5*x^2 - 2*x^3)^3. - _Colin Barker_, Feb 12 2019
%e A279972 Some solutions for n=4:
%e A279972 ..0..1..1. .0..1..0. .0..1..0. .0..1..0. .0..1..1. .0..1..1. .0..0..1
%e A279972 ..0..0..1. .1..1..1. .1..0..0. .1..1..1. .0..0..1. .0..1..1. .1..0..1
%e A279972 ..1..0..0. .0..0..1. .0..1..1. .0..0..1. .1..1..1. .1..0..0. .0..1..1
%e A279972 ..1..1..1. .1..1..0. .1..0..0. .0..0..1. .0..1..0. .1..1..0. .1..0..1
%Y A279972 Column 3 of A279977.
%K A279972 nonn
%O A279972 1,2
%A A279972 _R. H. Hardin_, Dec 24 2016