A148238 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, 1, 1), (0, 1, -1), (1, 0, 0)}.

1, 1, 2, 4, 13, 36, 105, 330, 1078, 3638, 11933, 41912, 145901, 516793, 1826389, 6645738, 24228599, 88225915, 325337560, 1210496127, 4526332777, 16879854659, 63732233744, 241458420405, 916751073403, 3485171083519, 13353360631538, 51292140290724, 197028744629141, 759800587109092, 2942586000346068

Offset

0,3

Links

Table of n, a(n) for n=0..30.

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, 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, 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: A151522 A148236 A148237 * A278281 A148239 A148240

Adjacent sequences: A148235 A148236 A148237 * A148239 A148240 A148241

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved