A148944 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), (0, 1, 1), (1, -1, 0), (1, 0, -1)}.

1, 1, 3, 9, 29, 103, 393, 1523, 5985, 24617, 102357, 430363, 1838761, 7931043, 34615153, 152208659, 673421637, 3003153451, 13464915837, 60712552141, 275067241835, 1251061909991, 5715825705399, 26206169918477, 120562798767589, 556428210284773, 2574906598392645, 11950271335525375, 55598176180817699

Offset

0,3

Links

Table of n, a(n) for n=0..28.

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[-1 + i, 1 + j, k, -1 + n] + aux[i, -1 + j, -1 + 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: A148942 A109432 A148943 * A293070 A060719 A091152

Adjacent sequences: A148941 A148942 A148943 * A148945 A148946 A148947

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved