A150432 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, 0, 1), (0, 1, 0), (1, -1, 1), (1, 1, 0)}.

1, 2, 7, 24, 98, 407, 1740, 7626, 34019, 154027, 702375, 3238330, 15036002, 70193322, 329372882, 1552973839, 7351786503, 34904153493, 166258508011, 794139913006, 3802027819251, 18240300341080, 87689544587124, 422337692525636, 2037180422979907, 9841473054662320, 47610988497196482, 230621686993480390

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, 1 + j, -1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[1 + i, 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: A363434 A150431 A302185 * A150433 A197554 A325581

Adjacent sequences: A150429 A150430 A150431 * A150433 A150434 A150435

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved