A150430 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, 1, 0), (0, 1, -1), (1, 0, 0), (1, 0, 1)}.

1, 2, 7, 24, 97, 401, 1692, 7409, 32894, 147976, 673011, 3091440, 14317001, 66635816, 312060730, 1469011146, 6939920335, 32907071979, 156569859687, 747072761700, 3573306593321, 17131688872318, 82316132903829, 396237598061021, 1910590572871349, 9227790455100265, 44633040691797814, 216164223668629316

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, j, -1 + k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, -1 + 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: A150427 A150428 A150429 * A363434 A150431 A302185

Adjacent sequences: A150427 A150428 A150429 * A150431 A150432 A150433

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved