A151084 Number of walks within N^3 (the first octant of Z^3) starting at (0,0,0) and consisting of n steps taken from {(-1, -1, -1), (-1, -1, 0), (0, 1, 1), (1, 0, 1), (1, 1, 0)}.

1, 3, 10, 43, 180, 794, 3594, 16281, 75560, 350968, 1647376, 7777248, 36838962, 175537404, 838148510, 4017672655, 19303611390, 92963938546, 448723447926, 2169464498226, 10508432340334, 50971062222142, 247592929032540, 1204164747873648, 5863164753277432, 28578855346427910, 139434574130451938

Offset

0,2

Links

Table of n, a(n) for n=0..26.

A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted Lattice Walks, ArXiv 0811.2899.

Mathematica

aux[i_Integer, j_Integer, k_Integer, n_Integer] := Which[Min[i, j, k, n] < 0 || Max[i, j, k] > n, 0, n == 0, KroneckerDelta[i, j, k, n], True, aux[i, j, k, n] = aux[-1 + i, -1 + j, k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[1 + i, 1 + j, k, -1 + n] + aux[1 + i, 1 + j, 1 + k, -1 + n]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]

Crossrefs

Sequence in context: A306237 A042545 A203266 * A151085 A082936 A347006

Adjacent sequences: A151081 A151082 A151083 * A151085 A151086 A151087

Keyword

nonn,walk,changed

Author

Manuel Kauers, Nov 18 2008

Status

approved