A149993 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), (-1, 1, -1), (0, 1, 0), (1, 0, 1)}.

1, 2, 5, 17, 59, 204, 755, 2886, 10983, 42642, 169339, 673729, 2696817, 10941944, 44610497, 182309217, 750649555, 3106888066, 12882897639, 53637560223, 224296097237, 939822049608, 3947315869157, 16633079275264, 70233934528157, 297056448537970, 1259315399665313, 5348993388208203

Offset

0,2

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, k, -1 + n] + aux[1 + 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: A278394 A056679 A084528 * A148413 A149994 A149995

Adjacent sequences: A149990 A149991 A149992 * A149994 A149995 A149996

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved