A150895 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, 0, 1), (0, 0, 1), (1, -1, 0), (1, 1, -1), (1, 1, 1)}.

1, 2, 8, 34, 155, 720, 3415, 16388, 79376, 386810, 1893990, 9307399, 45868921, 226559511, 1121063963, 5555392199, 27562783292, 136888378457, 680415457856, 3384453591042, 16844714507713, 83880626917644, 417879783643896, 2082604380577140, 10382601987269548, 51776341640782272, 258265723235989231

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, -1 + j, -1 + k, -1 + n] + aux[-1 + i, -1 + j, 1 + k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, 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: A150893 A235038 A150894 * A150896 A150897 A368763

Adjacent sequences: A150892 A150893 A150894 * A150896 A150897 A150898

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved