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

0,3

Links

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

Formula

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

Example

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

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 *)

Crossrefs

Cf. A106351.

Sequence in context: A221318 A221319 A221320 * A224916 A258321 A034791

Adjacent sequences: A221232 A221233 A221234 * A221236 A221237 A221238

Keyword

nonn

Author

R. H. Hardin, Jan 10 2013

Extensions

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

Status

approved