A148737 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, 0, 0), (-1, 1, 1), (0, -1, 1), (1, 0, -1), (1, 0, 0)}.

1, 1, 3, 7, 25, 84, 321, 1242, 4968, 20468, 85488, 365116, 1576455, 6899462, 30489198, 135943699, 610946248, 2764344098, 12585238942, 57609238284, 265003230438, 1224412614953, 5679988814414, 26445121892594, 123536478763163, 578852163791946, 2719950345757357, 12813842974436954, 60511380710167224

Offset

0,3

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, j, 1 + k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A366593 A148735 A148736 * A148738 A148739 A129084

Adjacent sequences: A148734 A148735 A148736 * A148738 A148739 A148740

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved