A148538 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, 0), (-1, 0, -1), (0, -1, 1), (0, 1, 1), (1, -1, -1)}.

1, 1, 3, 5, 19, 45, 161, 457, 1617, 5179, 17971, 61139, 216903, 762969, 2744373, 9872517, 36150073, 132105411, 487976897, 1811007517, 6765919223, 25368225627, 95571648291, 361732270303, 1374269046523, 5234143441549, 20015367671047, 76776227318671, 295363431102291, 1139028973260725, 4404632527328939

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, 1 + j, 1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, j, 1 + k, -1 + n] + aux[1 + i, 1 + 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: A148535 A148536 A148537 * A148539 A148540 A148541

Adjacent sequences: A148535 A148536 A148537 * A148539 A148540 A148541

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved