A148909 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, 1), (1, -1, 1), (1, 0, 1), (1, 1, -1)}.

1, 1, 3, 8, 32, 106, 432, 1606, 6832, 26873, 116447, 477181, 2099405, 8832030, 39290666, 168635917, 756571701, 3295972568, 14889850448, 65634238333, 298171048021, 1326776818628, 6055942572760, 27155773081241, 124446022092249, 561633552368125, 2582665008550517, 11719135008399185, 54052283604222045

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, 1 + k, -1 + n] + aux[-1 + 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, 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: A148906 A148907 A148908 * A148910 A148911 A148912

Adjacent sequences: A148906 A148907 A148908 * A148910 A148911 A148912

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved