A148046 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, 0, -1), (0, 1, 0), (1, -1, 0)}.

1, 1, 2, 3, 10, 20, 58, 129, 456, 1134, 3548, 9794, 33807, 96578, 306887, 967425, 3255598, 10137930, 32871380, 110954830, 371459199, 1212221590, 4058086695, 14072357534, 47559861357, 159489386798, 550988433164, 1927971427275, 6601530164918, 22631882518193, 79913196165907, 280987658710751, 973663407984038

Offset

0,3

Links

Table of n, a(n) for n=0..32.

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

Crossrefs

Sequence in context: A264038 A148044 A148045 * A148047 A148048 A148049

Adjacent sequences: A148043 A148044 A148045 * A148047 A148048 A148049

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved