A150403 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, 0, 0), (0, 0, 1), (1, 0, -1), (1, 1, 0)}.

1, 2, 7, 24, 93, 370, 1527, 6463, 27808, 121664, 538341, 2406850, 10855723, 49307861, 225460272, 1036492265, 4788796538, 22222484314, 103522304800, 483981651618, 2269814149608, 10676195116318, 50349168342481, 238021232167653, 1127753172950695, 5354295956275206, 25469536542093518, 121369374448402333

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, -1 + j, k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, j, 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: A026558 A150402 A151295 * A150404 A150405 A150406

Adjacent sequences: A150400 A150401 A150402 * A150404 A150405 A150406

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved