A149655 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, 1), (1, -1, 1), (1, 1, -1), (1, 1, 1)}.

1, 1, 5, 15, 75, 289, 1445, 6095, 30475, 135117, 675585, 3087987, 15439935, 72008619, 360043095, 1703029437, 8515147185, 40694381623, 203471908115, 979988489573, 4899942447865, 23742016308033, 118710081540165, 577930415357795, 2889652076788975, 14121788791089079, 70608943955445395, 346141784385418635

Offset

0,3

Links

Table of n, a(n) for n=0..27.

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, -1 + k, -1 + n] + aux[-1 + i, -1 + j, 1 + k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + 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: A101553 A149653 A149654 * A032122 A220818 A064678

Adjacent sequences: A149652 A149653 A149654 * A149656 A149657 A149658

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved