A148368 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), (-1, 0, 1), (0, 1, 1), (1, 0, -1)}.

1, 1, 2, 5, 16, 42, 147, 454, 1616, 5413, 20074, 69620, 266488, 954572, 3708394, 13683016, 53792464, 202506642, 806262279, 3080435321, 12385576657, 47967293239, 194245323577, 761125371583, 3102243729193, 12269768481988, 50309065115546, 200577969764539, 826529296034043, 3319155754364085

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[i, -1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A076958 A163825 A102866 * A148369 A148370 A148371

Adjacent sequences: A148365 A148366 A148367 * A148369 A148370 A148371

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved