A150457 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), (1, 0, 0), (1, 0, 1)}.

1, 2, 7, 25, 95, 390, 1620, 6965, 30522, 135385, 610014, 2771126, 12705652, 58683457, 272604795, 1273727257, 5977473827, 28170926189, 133252922101, 632302591304, 3009403153390, 14359827264254, 68684367797437, 329238009252576, 1581273797990676, 7608459327441592, 36669229629765119, 176998764917494340

Offset

0,2

Links

Table of n, a(n) for n=0..27.

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, 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: A150454 A150455 A150456 * A355628 A276903 A150458

Adjacent sequences: A150454 A150455 A150456 * A150458 A150459 A150460

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved