A149512 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, -1), (0, -1, 1), (1, -1, -1), (1, 1, 1)}.

1, 1, 5, 11, 47, 155, 589, 2243, 8705, 34179, 137203, 548507, 2227953, 9096849, 37321153, 154113155, 639423165, 2662177409, 11135243199, 46703001657, 196404723001, 828389701307, 3502233323823, 14838438328723, 63008334181707, 268053531545745, 1142430639590051, 4877227789503573

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, 1 + j, 1 + k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, j, 1 + 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: A149509 A149510 A149511 * A149513 A327494 A097743

Adjacent sequences: A149509 A149510 A149511 * A149513 A149514 A149515

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved