A149340 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, 0, 0), (-1, 0, 1), (0, -1, 0), (1, 1, -1), (1, 1, 0)}.

1, 1, 4, 12, 40, 154, 590, 2291, 9523, 39351, 164720, 711336, 3073150, 13376333, 59305585, 263251753, 1174914851, 5305026397, 23991323059, 108935348192, 498558014381, 2285348450639, 10508708646670, 48595333492782, 225057299921016, 1044912400895195, 4871739738152142, 22745133446781661

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, -1 + j, k, -1 + n] + aux[-1 + i, -1 + j, 1 + k, -1 + n] + aux[i, 1 + j, k, -1 + n] + aux[1 + i, j, -1 + k, -1 + n] + aux[1 + i, 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: A149337 A149338 A149339 * A246317 A180889 A002996

Adjacent sequences: A149337 A149338 A149339 * A149341 A149342 A149343

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved