A148594 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, 0, 0), (-1, 1, 1), (0, 0, -1), (1, 0, 0)}.

1, 1, 3, 6, 20, 57, 196, 652, 2305, 8187, 29938, 110468, 415523, 1576423, 6054903, 23444901, 91538346, 359866575, 1424136635, 5667087376, 22676094964, 91152587752, 368075554103, 1492157429875, 6072007615541, 24792251075928, 101557819189515, 417226553637568, 1718945886662743

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[i, j, 1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A148591 A148592 A148593 * A148595 A214821 A148596

Adjacent sequences: A148591 A148592 A148593 * A148595 A148596 A148597

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved