A148681 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, 0), (-1, -1, 1), (-1, 0, -1), (0, 1, -1), (1, 0, 1)}.

1, 1, 3, 7, 22, 66, 227, 748, 2710, 9643, 35646, 133338, 506112, 1938692, 7546335, 29463016, 116453080, 462871956, 1851092051, 7451911578, 30144766089, 122486787548, 500198189286, 2049540237382, 8430872633779, 34799109527697, 144055056806443, 598143461783294, 2490167439891266

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, j, -1 + k, -1 + n] + aux[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, 1 + 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: A036719 A166135 A007595 * A148682 A148683 A148684

Adjacent sequences: A148678 A148679 A148680 * A148682 A148683 A148684

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved