A149818 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, 1, -1), (0, 0, 1), (0, 1, 0), (1, -1, -1)}.

1, 2, 4, 10, 26, 76, 248, 824, 2766, 9616, 34586, 126604, 469054, 1763768, 6740582, 26050180, 101538790, 399330656, 1585705250, 6344919988, 25545244242, 103470060008, 421830613640, 1729216715736, 7121389942094, 29457398594096, 122424027677428, 510904322626572, 2139753669413014

Offset

0,2

Links

Table of n, a(n) for n=0..28.

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[i, -1 + j, k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, -1 + 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: A149815 A149816 A149817 * A148101 A052854 A148102

Adjacent sequences: A149815 A149816 A149817 * A149819 A149820 A149821

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved