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

0,8

Links

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

Example

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

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 *)

Crossrefs

Column k=1 of A286216.

Column k=2 of A307796.

Sequence in context: A338706 A338710 A336516 * A293797 A179608 A340686

Adjacent sequences: A286206 A286207 A286208 * A286210 A286211 A286212

Keyword

nonn

Author

R. H. Hardin, May 04 2017

Status

approved