A149832 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), (0, 0, 1), (1, -1, 1), (1, 0, 0)}.

1, 2, 4, 10, 28, 87, 295, 1025, 3668, 13505, 50939, 195811, 765060, 3032505, 12164349, 49338483, 202003995, 834137367, 3470745959, 14540711868, 61299117863, 259882257795, 1107518408090, 4742237074597, 20394709933666, 88065138323178, 381695490302277, 1660121541256698, 7243858826868699

Offset

0,2

Links

Table of n, a(n) for n=0..28.

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, k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[i, 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: A027412 A030277 A149831 * A229046 A363110 A271207

Adjacent sequences: A149829 A149830 A149831 * A149833 A149834 A149835

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved