A151085 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), (0, 1, 1), (1, 0, 1), (1, 1, 0)}.

1, 3, 10, 43, 182, 803, 3635, 16537, 76742, 357427, 1678899, 7932323, 37617702, 179305425, 856913256, 4108608935, 19750080914, 95143303843, 459343861243, 2221416227189, 10761044080978, 52205865641821, 253606546956982, 1233519006840273, 6006367583321020, 29277410062467563, 142846687651530691

Offset

0,2

Links

Table of n, a(n) for n=0..26.

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, k, -1 + n] + aux[-1 + i, j, -1 + 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, 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: A042545 A203266 A151084 * A082936 A347006 A205487

Adjacent sequences: A151082 A151083 A151084 * A151086 A151087 A151088

Keyword

nonn,walk,changed

Author

Manuel Kauers, Nov 18 2008

Status

approved