A150475 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), (0, 1, -1), (0, 1, 1), (1, -1, 0)}.

1, 2, 7, 25, 99, 407, 1736, 7584, 33771, 152633, 697966, 3222902, 15000588, 70287630, 331218105, 1568416959, 7458237045, 35596100785, 170438383971, 818403513883, 3939723976715, 19008401989542, 91898156436871, 445105730900628, 2159434063875192, 10492328046710094, 51050700215626557, 248701904388999187

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[i, -1 + j, -1 + k, -1 + n] + aux[i, -1 + j, 1 + 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: A150472 A150473 A150474 * A150476 A150477 A333249

Adjacent sequences: A150472 A150473 A150474 * A150476 A150477 A150478

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved