A149498 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, -1, 0), (-1, 1, -1), (1, -1, -1), (1, 1, 1)}.

1, 1, 5, 9, 45, 109, 509, 1517, 6757, 22461, 98997, 345653, 1529269, 5506201, 24429845, 90301037, 400891885, 1513502725, 6723798125, 25795029197, 114713713765, 445819303429, 1984246519061, 7797336046153, 34724021189789, 137746829186609, 613736119949989, 2454296224465553, 10940223238022509

Offset

0,3

Links

Table of n, a(n) for n=0..28.

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, 1 + j, 1 + k, -1 + n] + aux[1 + i, -1 + j, 1 + k, -1 + n] + aux[1 + i, 1 + j, 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: A121724 A149496 A149497 * A149499 A100305 A149500

Adjacent sequences: A149495 A149496 A149497 * A149499 A149500 A149501

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved