A151107 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), (0, 0, 1), (0, 1, -1), (0, 1, 0), (1, 0, 1)}.

1, 3, 11, 44, 189, 836, 3775, 17340, 80636, 378332, 1788088, 8501974, 40620628, 194858456, 937964265, 4528198964, 21915789948, 106302387911, 516614920778, 2514951710592, 12261659627080, 59862759662348, 292612161474242, 1431874250076864, 7013747159996448, 34386620331167998, 168728800332946336

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, j, -1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[i, 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: A389410 A151106 A302186 * A063018 A293468 A151108

Adjacent sequences: A151104 A151105 A151106 * A151108 A151109 A151110

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved