A148251 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, 1, 0), (1, -1, 1), (1, 0, -1), (1, 0, 0)}.

1, 1, 2, 4, 13, 36, 124, 397, 1485, 5181, 20291, 75144, 303886, 1173749, 4865351, 19393235, 81893553, 334492176, 1433581525, 5969863058, 25895103318, 109543497246, 479893948780, 2056616543073, 9085105169193, 39360938959297, 175113080083898, 765717107275926, 3427433582855374

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, 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] + 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: A148248 A148249 A148250 * A144924 A148252 A268698

Adjacent sequences: A148248 A148249 A148250 * A148252 A148253 A148254

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved