A149567 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), (-1, 0, 1), (1, 0, -1), (1, 1, 1)}

1, 1, 5, 13, 61, 201, 945, 3453, 16293, 63145, 298781, 1202799, 5703523, 23577447, 111992747, 472089081, 2245549141, 9608529475, 45757357387, 198121904171, 944424232919, 4128557781623, 19697281953755, 86790670454669, 414390032409781, 1838063755309025, 8781911972684573, 39173855467598759

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, j, 1 + k, -1 + n] + aux[1 + i, 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: A284035 A051859 A151275 * A149568 A201805 A144725

Adjacent sequences: A149564 A149565 A149566 * A149568 A149569 A149570

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved