A148480 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, 1), (0, 0, 1), (1, -1, 1), (1, 1, -1)}.

1, 1, 2, 6, 20, 71, 281, 1123, 4752, 20252, 88984, 393523, 1772005, 8023052, 36748575, 169092971, 784207581, 3650862063, 17092352795, 80278975116, 378632852454, 1790653312523, 8495800530735, 40401419781113, 192619376329586, 920148244891016, 4404737154447986, 21121154511469402, 101453501272499919

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, 1 + j, -1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, -1 + 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: A163134 A370446 A150128 * A194950 A150129 A360267

Adjacent sequences: A148477 A148478 A148479 * A148481 A148482 A148483

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved