A148532 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, 0, 1), (-1, 1, -1), (-1, 1, 0), (1, 0, 0)}.

1, 1, 3, 5, 19, 39, 165, 377, 1675, 4079, 18697, 47563, 222459, 584011, 2770685, 7449705, 35708087, 97825139, 472520197, 1314174063, 6385336303, 17980498927, 87768137549, 249725121217, 1223468145825, 3511930248569, 17256964295705, 49912442579597, 245855762926615, 715788698299345, 3532860855298281

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, k, -1 + n] + aux[1 + i, -1 + j, k, -1 + n] + aux[1 + i, -1 + j, 1 + k, -1 + n] + aux[1 + i, 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: A148529 A148530 A148531 * A148533 A242818 A218373

Adjacent sequences: A148529 A148530 A148531 * A148533 A148534 A148535

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved