A149519 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, 0), (-1, 1, -1), (1, -1, -1), (1, 1, 1)}.

1, 1, 5, 11, 49, 157, 681, 2371, 10745, 39323, 179183, 689829, 3166221, 12438603, 57683523, 231728067, 1077569125, 4402483823, 20583007623, 85034398167, 398951873741, 1668087724597, 7844558761569, 33069790913997, 155992820970213, 662633252179911, 3131081805336965, 13392143350370781

Offset

0,3

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, -1 + j, -1 + k, -1 + n] + aux[-1 + i, 1 + j, 1 + k, -1 + n] + aux[1 + i, -1 + j, 1 + k, -1 + n] + aux[1 + i, j, 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: A149516 A149517 A149518 * A149520 A073415 A176832

Adjacent sequences: A149516 A149517 A149518 * A149520 A149521 A149522

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved