A148692 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, 0, -1), (1, 0, 1)}.

1, 1, 3, 7, 23, 66, 227, 713, 2577, 8568, 31421, 107380, 402624, 1417736, 5348491, 19083805, 72852019, 264474288, 1012997899, 3707123478, 14304055198, 52928721410, 204637258329, 761248539668, 2957838935076, 11088044278984, 43138654656074, 162322972687620, 633772214576506, 2398222243714200

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[-1 + i, j, 1 + 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: A148689 A148690 A148691 * A201204 A106964 A096019

Adjacent sequences: A148689 A148690 A148691 * A148693 A148694 A148695

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved