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.

0, 0, 0, 0, 0, 0, 1, 3, 10, 24, 60, 134, 304, 656, 1420, 2996, 6312, 13112, 27167, 55825, 114412, 233282, 474563, 962159, 1947098, 3931288, 7925708, 15952866, 32072580, 64404708, 129213082, 259009006, 518818124, 1038549912, 2077775396, 4154785904, 8304424080

Offset: 0

Author

R. H. Hardin, May 04 2017

Keywords

• nonn

Examples

			All solutions for n=7
..0. .0. .0
..1. .0. .1
..0. .1. .0
..0. .0. .0
..0. .0. .1
..1. .1. .0
..0. .0. .0
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..3327 (terms n = 1..210 from R. H. Hardin)

Crossrefs

Column k=1 of A286216.

Column k=2 of A307796.

Programs

Maple

b:= proc(n, t, h, c) option remember; `if`(abs(c-2)>n, 0, `if`(n=0, 1,
      b(n-1, [1, 3, 1][t], 2, c-`if`(h=3, 1, 0))+
      b(n-1, 2, [1, 3, 1][h], c+`if`(t=3, 1, 0))))
    end:
a:= n-> b(n, 1$2, 0):
seq(a(n), n=0..40);  # Alois P. Heinz, Apr 29 2019

Mathematica

b[n_, t_, h_, c_] := b[n, t, h, c] = If[Abs[c - 2] > n, 0, If[n == 0, 1,
     b[n - 1, {1, 3, 1}[[t]], 2, c - If[h == 3, 1, 0]] +
     b[n - 1, 2, {1, 3, 1}[[h]], c + If[t == 3, 1, 0]]]];
a[n_] := b[n, 1, 1, 0];
Table[a[n], {n, 0, 40}] (* Jean-François Alcover, Jun 27 2022, after Alois P. Heinz *)