A149478 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), (-1, 1, 0), (1, -1, 0), (1, 0, 1), (1, 1, -1)}.

1, 1, 4, 13, 57, 223, 1028, 4392, 20801, 93192, 448388, 2068395, 10052266, 47272935, 231307163, 1102408601, 5419992341, 26082078971, 128680642305, 623701125067, 3085177756781, 15035715248503, 74523449457592, 364745828732076, 1810638694267339, 8891946466493735, 44194574931517811, 217627063614150518

Offset

0,3

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, -1 + j, 1 + k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[1 + i, -1 + j, 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: A304670 A316117 A149477 * A149479 A149480 A151481

Adjacent sequences: A149475 A149476 A149477 * A149479 A149480 A149481

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved