A149798 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, 0, 1), (1, -1, 0), (1, 1, -1), (1, 1, 1)}

1, 1, 5, 19, 87, 361, 1725, 7687, 37101, 170795, 834677, 3932441, 19303463, 92161037, 454658169, 2193047187, 10845000033, 52668165919, 261103799245, 1275006361955, 6329800166463, 31031356285737, 154272833422475, 758780915471777, 3775619464304719, 18616082621972999, 92711332843558493

Offset

0,3

Links

Table of n, a(n) for n=0..26.

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, k, -1 + n] + aux[1 + i, 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: A275027 A147091 A149797 * A149799 A149800 A147099

Adjacent sequences: A149795 A149796 A149797 * A149799 A149800 A149801

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved