A149925 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, 1, 0), (0, 0, 1), (1, 0, 0)}.

1, 2, 5, 15, 47, 163, 581, 2127, 7979, 30353, 117875, 462727, 1835691, 7345512, 29607177, 120261572, 491251251, 2017406965, 8322270169, 34475449031, 143385518330, 598369350109, 2504936815151, 10515729895021, 44261703490891, 186758143456491, 789756587969833, 3346574844955685

Offset

0,2

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, j, k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, -1 + 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: A149923 A219231 A149924 * A149926 A321467 A301994

Adjacent sequences: A149922 A149923 A149924 * A149926 A149927 A149928

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved