A221235 Number of nonnegative integer arrays of length n summing to n without adjacent equal values.

1, 1, 2, 7, 14, 30, 76, 188, 444, 1075, 2656, 6504, 15926, 39316, 97252, 240597, 596686, 1482971, 3689768, 9191590, 22927718, 57253334, 143101896, 358003469, 896391914, 2246149936, 5632310800, 14132640565, 35483595966, 89141668532, 224061612932, 563473301874

Offset: 0

Author

R. H. Hardin, Jan 10 2013

Keywords

• nonn

Examples

			All solutions for n=3
..1....2....0....2....0....0....1
..2....1....3....0....2....1....0
..0....0....0....1....1....2....2
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..500 (first 210 terms from R. H. Hardin)

Crossrefs

Cf. A106351.

Programs

Maple

b:= proc(n, h, t) option remember; `if`(t<2, `if`(n<>h, 1, 0),
      add(`if`(h=j, 0, b(n-j, `if`(j>n-j, -1, j), t-1)), j=0..n))
    end:
a:= n-> b(n, -1, n):
seq(a(n), n=0..35);  # Alois P. Heinz, Oct 15 2017

Mathematica

b[n_, h_, t_] := b[n, h, t] = If[t < 2, If[n != h, 1, 0],
     Sum[If[h == j, 0, b[n-j, If[j > n-j, -1, j], t-1]], {j, 0, n}]];
a[n_] := b[n, -1, n];
Table[a[n], {n, 0, 35}] (* Jean-François Alcover, Apr 28 2022, after Alois P. Heinz *)

Formula

a(n) = A106351(2n,n). - Alois P. Heinz, Oct 12 2017

Extensions

a(0)=1 prepended by Alois P. Heinz, Oct 15 2017