A149248 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, 0), (1, -1, 1), (1, 1, 0)}.

1, 1, 4, 11, 38, 127, 469, 1677, 6378, 24095, 93609, 362445, 1436332, 5676421, 22781348, 91416871, 370922058, 1504651077, 6159395169, 25221691069, 103977918900, 428932959075, 1779227261594, 7385144690729, 30792699917314, 128496500238255, 538174185677349, 2255895860083435, 9485551742409292

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, k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[-1 + i, 1 + j, 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: A027573 A149246 A149247 * A149249 A149250 A149251

Adjacent sequences: A149245 A149246 A149247 * A149249 A149250 A149251

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved