A149355 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, 0), (-1, 0, 1), (0, 0, -1), (0, 1, -1), (1, 0, 1)}.

1, 1, 4, 12, 43, 145, 597, 2275, 9074, 37089, 156211, 648877, 2751041, 11870673, 51348956, 222248568, 975497005, 4308619931, 19026532763, 84456709317, 377858527555, 1693033357949, 7596253980354, 34265491415383, 155101324617082, 702483816158325, 3190205461239309, 14540514604960278

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, j, -1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[1 + i, j, -1 + k, -1 + n] + aux[1 + i, 1 + j, 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: A292287 A003444 A220881 * A149356 A149357 A149358

Adjacent sequences: A149352 A149353 A149354 * A149356 A149357 A149358

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved