A149036 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, 0), (0, 1, 1), (1, -1, 1), (1, 0, -1)}.

1, 1, 3, 10, 35, 126, 495, 1973, 8009, 33248, 139542, 592995, 2548398, 11028950, 48080272, 210957689, 930544023, 4125086990, 18365051708, 82072860679, 368080787422, 1656042383739, 7472205409603, 33804828156837, 153307934411980, 696826434016249, 3173884743217481, 14484245585420602

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, 1 + j, -1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A300975 A072266 A085282 * A316596 A047127 A114196

Adjacent sequences: A149033 A149034 A149035 * A149037 A149038 A149039

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved