A149819 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), (0, 0, -1), (0, 1, 0), (1, 0, 0)}.

1, 2, 4, 10, 28, 80, 240, 756, 2424, 7904, 26368, 89324, 305480, 1056480, 3693280, 13011712, 46144768, 164775296, 592005184, 2137741872, 7754971680, 28258590336, 103392253824, 379649300944, 1398639670240, 5168935430656, 19158863140288, 71201979973480, 265265435150064, 990589140446528, 3707399290547776

Offset

0,2

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, j, k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[i, j, 1 + 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: A271896 A148109 A099216 * A276051 A149820 A149821

Adjacent sequences: A149816 A149817 A149818 * A149820 A149821 A149822

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved