A149635 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), (-1, 0, 1), (1, 0, -1), (1, 1, 1)}.

1, 1, 5, 15, 69, 233, 1123, 4193, 20365, 79577, 389657, 1576461, 7753541, 32101097, 158408649, 667616317, 3302236011, 14108958387, 69912164165, 302004643089, 1498550596927, 6531886516731, 32446754425099, 142495425257375, 708461316243015, 3131209264861149, 15579022833875687, 69232956490530607

Offset

0,3

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, -1 + k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[1 + 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: A149632 A149633 A149634 * A149636 A149637 A149638

Adjacent sequences: A149632 A149633 A149634 * A149636 A149637 A149638

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved