A149358 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, 1, 0), (0, 1, -1), (1, 0, -1), (1, 0, 1)}.

1, 1, 4, 12, 43, 163, 656, 2698, 11344, 48724, 212399, 939687, 4195518, 18895902, 85815964, 392491390, 1804983326, 8343871333, 38761066926, 180795136179, 846325495536, 3975432440478, 18731970424992, 88502758036004, 419206009153425, 1990366204167853, 9470375008073564, 45149095508017120

Offset

0,3

Links

Table of n, a(n) for n=0..27.

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[-1 + i, j, 1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, -1 + 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: A149355 A149356 A149357 * A149359 A259223 A167402

Adjacent sequences: A149355 A149356 A149357 * A149359 A149360 A149361

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved