A148342 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), (-1, 0, 0), (0, 1, 1), (1, 0, -1)}.

1, 1, 2, 5, 15, 39, 127, 405, 1318, 4466, 15550, 53884, 193390, 695626, 2533119, 9358466, 34732921, 129973012, 491079718, 1861380970, 7112950619, 27328619931, 105348098378, 408522462226, 1590208842894, 6211513530538, 24376104902326, 95919408177971, 378610755658316, 1499595517271958, 5953738889365696

Offset

0,3

Links

Table of n, a(n) for n=0..30.

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, 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: A242823 A059840 A280064 * A148343 A148344 A148345

Adjacent sequences: A148339 A148340 A148341 * A148343 A148344 A148345

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved