A148958 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), (0, 1, -1), (1, -1, 1), (1, 0, 1)}.

1, 1, 3, 9, 30, 106, 404, 1537, 6162, 24766, 102397, 426210, 1802081, 7664693, 33007543, 142705843, 622404766, 2725693390, 12012620447, 53129180250, 236136223997, 1052733359943, 4711947945784, 21146457395624, 95204483953282, 429645241238136, 1944091905593840, 8815083658503187, 40060085756852042

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, -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, -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: A316371 A181933 A148957 * A024332 A036727 A216454

Adjacent sequences: A148955 A148956 A148957 * A148959 A148960 A148961

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved