A150309 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, 0, 1), (-1, 1, -1), (1, 0, 0), (1, 0, 1)}.

1, 2, 7, 21, 85, 294, 1272, 4747, 21315, 83292, 382779, 1543270, 7203739, 29703453, 140199473, 588006685, 2798356537, 11893946434, 56963151145, 244726987219, 1177917607078, 5105618498090, 24673112135212, 107742163605567, 522384189440122, 2295641395412240, 11160862178717788, 49316058297555925

Offset

0,2

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, j, 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, 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: A150307 A321283 A150308 * A150310 A150311 A150312

Adjacent sequences: A150306 A150307 A150308 * A150310 A150311 A150312

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved