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A286209 Number of n X 1 0..1 arrays with the number of 1's king-move adjacent to some 0 two less than the number of 0's adjacent to some 1.

%I A286209 #20 Jun 27 2022 07:49:57
%S A286209 0,0,0,0,0,0,1,3,10,24,60,134,304,656,1420,2996,6312,13112,27167,
%T A286209 55825,114412,233282,474563,962159,1947098,3931288,7925708,15952866,
%U A286209 32072580,64404708,129213082,259009006,518818124,1038549912,2077775396,4154785904,8304424080
%N A286209 Number of n X 1 0..1 arrays with the number of 1's king-move adjacent to some 0 two less than the number of 0's adjacent to some 1.
%H A286209 Alois P. Heinz, <a href="/A286209/b286209.txt">Table of n, a(n) for n = 0..3327</a> (terms n = 1..210 from R. H. Hardin)
%e A286209 All solutions for n=7
%e A286209 ..0. .0. .0
%e A286209 ..1. .0. .1
%e A286209 ..0. .1. .0
%e A286209 ..0. .0. .0
%e A286209 ..0. .0. .1
%e A286209 ..1. .1. .0
%e A286209 ..0. .0. .0
%p A286209 b:= proc(n, t, h, c) option remember; `if`(abs(c-2)>n, 0, `if`(n=0, 1,
%p A286209       b(n-1, [1, 3, 1][t], 2, c-`if`(h=3, 1, 0))+
%p A286209       b(n-1, 2, [1, 3, 1][h], c+`if`(t=3, 1, 0))))
%p A286209     end:
%p A286209 a:= n-> b(n, 1$2, 0):
%p A286209 seq(a(n), n=0..40);  # _Alois P. Heinz_, Apr 29 2019
%t A286209 b[n_, t_, h_, c_] := b[n, t, h, c] = If[Abs[c - 2] > n, 0, If[n == 0, 1,
%t A286209      b[n - 1, {1, 3, 1}[[t]], 2, c - If[h == 3, 1, 0]] +
%t A286209      b[n - 1, 2, {1, 3, 1}[[h]], c + If[t == 3, 1, 0]]]];
%t A286209 a[n_] := b[n, 1, 1, 0];
%t A286209 Table[a[n], {n, 0, 40}] (* _Jean-François Alcover_, Jun 27 2022, after _Alois P. Heinz_ *)
%Y A286209 Column k=1 of A286216.
%Y A286209 Column k=2 of A307796.
%K A286209 nonn
%O A286209 0,8
%A A286209 _R. H. Hardin_, May 04 2017