A148776 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), (0, -1, 0), (0, 1, -1), (1, 0, 1)}.

1, 1, 3, 8, 23, 70, 231, 747, 2519, 8596, 30022, 104652, 372171, 1327738, 4795592, 17329563, 63304887, 231602170, 853989048, 3150826452, 11704071278, 43519371188, 162687329027, 608474865891, 2286424185195, 8597775368680, 32455844916962, 122568464638204, 464459733245576, 1760989548140200

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, j, -1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[i, 1 + j, 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: A061557 A000782 A148775 * A353067 A127385 A152880

Adjacent sequences: A148773 A148774 A148775 * A148777 A148778 A148779

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved