A148459 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, 0), (0, -1, 1), (0, 0, 1), (1, 1, -1)}.

1, 1, 2, 6, 18, 57, 198, 709, 2601, 9864, 38148, 149808, 598372, 2419970, 9889001, 40838480, 170083988, 713613807, 3015878875, 12823991428, 54829658278, 235678930783, 1017743418774, 4413589486399, 19218488856579, 83989136588578, 368284554761549, 1620125911384969, 7147971908460116

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, -1 + j, 1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, j, 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: A369621 A273203 A148458 * A324166 A355388 A351787

Adjacent sequences: A148456 A148457 A148458 * A148460 A148461 A148462

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved