A149010 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, 0, 0), (-1, 1, 1), (0, -1, 1), (0, 1, 1), (1, 1, -1)}.

1, 1, 3, 9, 34, 125, 493, 1985, 8180, 34302, 145926, 627524, 2726280, 11936938, 52633883, 233489865, 1041206147, 4664657374, 20984288491, 94744961342, 429195209302, 1950061381214, 8884153679617, 40574888499106, 185729217351340, 851933251755367, 3915290059172227, 18025719113319250

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[i, -1 + j, -1 + k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A007722 A149008 A149009 * A149011 A149012 A145090

Adjacent sequences: A149007 A149008 A149009 * A149011 A149012 A149013

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved