A148103 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, 1, 0), (0, 0, 1), (0, 1, -1), (1, -1, 0)}.

1, 1, 2, 4, 10, 26, 81, 244, 819, 2695, 9463, 32922, 120808, 437836, 1659640, 6217694, 24120576, 92725987, 366692792, 1438275924, 5781789727, 23060129968, 93964095455, 380158396326, 1566773918574, 6416020471974, 26705782715536, 110498732504920, 463940330488819, 1937038870676946

Offset

0,3

Links

Table of n, a(n) for n=0..29.

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, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, -1 + 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: A195924 A116673 A135410 * A148104 A179981 A086991

Adjacent sequences: A148100 A148101 A148102 * A148104 A148105 A148106

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved