A149249 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), (0, 0, -1), (1, 0, 1)}.

1, 1, 4, 11, 38, 127, 469, 1705, 6406, 24361, 94379, 367885, 1448670, 5757657, 23036942, 92690393, 375046694, 1525796861, 6232717793, 25559071943, 105212294444, 434576923263, 1800291921582, 7478809262827, 31152816275990, 130077849792829, 544339365292115, 2282722021782731, 9591885050778532

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, -1 + k, -1 + n] + aux[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: A149246 A149247 A149248 * A149250 A149251 A149252

Adjacent sequences: A149246 A149247 A149248 * A149250 A149251 A149252

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved