A150140 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, 0, 0), (0, -1, 0), (0, 0, 1), (0, 1, 0), (1, 1, -1)}.

1, 2, 6, 20, 73, 280, 1119, 4596, 19322, 82650, 358876, 1576911, 7001693, 31358107, 141524444, 642918451, 2937880585, 13493909464, 62267058197, 288513529181, 1341856939676, 6261982534246, 29313304996458, 137606976791765, 647659389106798, 3055539614439363, 14447445331063563, 68451237108563191

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, -1 + j, 1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[i, 1 + j, k, -1 + n] + aux[1 + i, 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: A148481 A150139 A052884 * A061396 A230823 A192497

Adjacent sequences: A150137 A150138 A150139 * A150141 A150142 A150143

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved