A149287 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, 0, 0), (0, 1, -1), (1, -1, 1), (1, 1, 0)}

1, 1, 4, 11, 44, 163, 665, 2746, 11685, 50560, 222560, 990647, 4461545, 20261605, 92750052, 427391693, 1980932854, 9228373502, 43188083319, 202928074526, 956967526605, 4527549376056, 21483545535985, 102213596708559, 487492635095972, 2330199032630362, 11161042429983908, 53558921980348752

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, k, -1 + n] + aux[-1 + i, 1 + 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]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]

Crossrefs

Sequence in context: A149284 A149285 A149286 * A149288 A149289 A149290

Adjacent sequences: A149284 A149285 A149286 * A149288 A149289 A149290

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved