A149926 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, 1), (-1, 1, -1), (0, 1, 0), (1, 0, 0)}.

1, 2, 5, 15, 47, 163, 586, 2160, 8143, 31249, 122003, 482213, 1924812, 7746184, 31413375, 128260561, 526691085, 2173416903, 9007876762, 37483502040, 156541737992, 655875059098, 2755922252710, 11610743967840, 49035694269000, 207557684051887, 880354998513425, 3741090893585575

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

Crossrefs

Sequence in context: A219231 A149924 A149925 * A321467 A301994 A289589

Adjacent sequences: A149923 A149924 A149925 * A149927 A149928 A149929

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved