A149077 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), (0, -1, -1), (1, 1, 1)}.

1, 1, 4, 7, 28, 70, 244, 751, 2356, 8122, 25684, 89506, 297424, 1000768, 3500152, 11753635, 41555116, 142721506, 494942476, 1752770218, 6058733488, 21640017244, 75771413032, 267205134886, 955330818784, 3358717350628, 12087889213456, 42861039690400, 152805077511136, 550266294379468, 1956458666266096

Offset

0,3

Links

Table of n, a(n) for n=0..30.

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, 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: A149076 A383603 A123767 * A149078 A149079 A149080

Adjacent sequences: A149074 A149075 A149076 * A149078 A149079 A149080

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved