A148440 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, -1, 1), (-1, 0, 0), (0, 1, 1), (1, 0, -1)}.

1, 1, 2, 6, 16, 45, 154, 499, 1634, 5888, 20672, 73593, 274009, 1005519, 3759072, 14335509, 54252692, 208982781, 811404178, 3144286752, 12352600466, 48645794723, 191989283484, 764771646799, 3048041384831, 12199723310941, 49103289442878, 197753021277819, 800089083193025, 3247148044051183

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, k, -1 + n] + aux[1 + i, 1 + 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: A290953 A151391 A166896 * A148441 A307606 A098617

Adjacent sequences: A148437 A148438 A148439 * A148441 A148442 A148443

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved