|
%I #20 Jun 27 2022 07:49:57
%S 0,0,0,0,0,0,1,3,10,24,60,134,304,656,1420,2996,6312,13112,27167,
%T 55825,114412,233282,474563,962159,1947098,3931288,7925708,15952866,
%U 32072580,64404708,129213082,259009006,518818124,1038549912,2077775396,4154785904,8304424080
%N 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 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 All solutions for n=7
%e ..0. .0. .0
%e ..1. .0. .1
%e ..0. .1. .0
%e ..0. .0. .0
%e ..0. .0. .1
%e ..1. .1. .0
%e ..0. .0. .0
%p b:= proc(n, t, h, c) option remember; `if`(abs(c-2)>n, 0, `if`(n=0, 1,
%p b(n-1, [1, 3, 1][t], 2, c-`if`(h=3, 1, 0))+
%p b(n-1, 2, [1, 3, 1][h], c+`if`(t=3, 1, 0))))
%p end:
%p a:= n-> b(n, 1$2, 0):
%p seq(a(n), n=0..40); # _Alois P. Heinz_, Apr 29 2019
%t b[n_, t_, h_, c_] := b[n, t, h, c] = If[Abs[c - 2] > n, 0, If[n == 0, 1,
%t b[n - 1, {1, 3, 1}[[t]], 2, c - If[h == 3, 1, 0]] +
%t b[n - 1, 2, {1, 3, 1}[[h]], c + If[t == 3, 1, 0]]]];
%t a[n_] := b[n, 1, 1, 0];
%t Table[a[n], {n, 0, 40}] (* _Jean-François Alcover_, Jun 27 2022, after _Alois P. Heinz_ *)
%Y Column k=1 of A286216.
%Y Column k=2 of A307796.
%K nonn
%O 0,8
%A _R. H. Hardin_, May 04 2017
|
