A148757 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, 1), (-1, 1, 1), (1, 0, -1), (1, 0, 0)}

1, 1, 3, 7, 28, 80, 343, 1109, 4957, 17265, 79054, 289714, 1348498, 5126901, 24142264, 94383071, 448304541, 1791386504, 8565590298, 34836181497, 167448617851, 690969359292, 3335440944368, 13931963736742, 67487310816370, 284820772882426, 1383712783056099, 5891971199940838, 28694836974139199

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[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, j, -1 + 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: A148756 A352701 A351771 * A148758 A054277 A197960

Adjacent sequences: A148754 A148755 A148756 * A148758 A148759 A148760

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved