A148104 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, 0, 1), (0, 1, -1), (1, -1, 0)}.

1, 1, 2, 4, 10, 26, 81, 249, 829, 2781, 9734, 34536, 126493, 467981, 1772281, 6773484, 26300887, 103087732, 408575953, 1633521878, 6587707484, 26766158187, 109535161586, 451095906037, 1868996075017, 7786154256547, 32603467462740, 137177326830502, 579721759893509, 2460236646799349

Offset

0,3

Links

Table of n, a(n) for n=0..29.

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[i, -1 + j, 1 + k, -1 + n] + aux[i, 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: A116673 A135410 A148103 * A179981 A086991 A272603

Adjacent sequences: A148101 A148102 A148103 * A148105 A148106 A148107

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved