A149562 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, 0), (-1, 1, 1), (1, 0, -1), (1, 1, 1)}

1, 1, 5, 13, 59, 197, 899, 3309, 15477, 59713, 284057, 1132297, 5429661, 22193239, 106957103, 445369365, 2156332451, 9104878879, 44258847303, 188981432661, 921420662873, 3971513351725, 19409177178657, 84322950285615, 412904631879695, 1805941947909049, 8858223727277157, 38968453636590119

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, -1 + j, -1 + k, -1 + n] + aux[1 + i, 1 + 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: A149559 A149560 A149561 * A149563 A149564 A149565

Adjacent sequences: A149559 A149560 A149561 * A149563 A149564 A149565

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved