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A148678 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, 0), (0, 0, -1), (1, 0, 1)} 0
1, 1, 3, 7, 21, 73, 229, 761, 2671, 9387, 34743, 127299, 462043, 1736519, 6577091, 25138527, 96964869, 371447721, 1437904717, 5632450065, 22114602041, 87321019245, 344916017793, 1364490574293, 5439723894253, 21765386886513, 87302393318629, 350941102667225, 1411395747080789, 5695892893180473 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..29.

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, j, 1 + k, -1 + n] + aux[1 + i, -1 + j, 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: A037127 A105795 A244174 * A148679 A148680 A001576

Adjacent sequences:  A148675 A148676 A148677 * A148679 A148680 A148681

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified November 18 05:08 EST 2017. Contains 294853 sequences.