A149764 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), (0, -1, 1), (1, -1, 0), (1, 0, -1), (1, 1, 1)}.

1, 1, 5, 19, 73, 299, 1265, 5435, 23641, 103813, 460001, 2052807, 9213259, 41554885, 188228345, 855734883, 3902932219, 17852219099, 81867457369, 376297840835, 1733227480133, 7998362063665, 36974103353355, 171192071662033, 793788595642235, 3685643977371843, 17134313003875339, 79749310147234405

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, 1 + j, k, -1 + n] + aux[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: A287805 A129166 A149763 * A149765 A124464 A149766

Adjacent sequences: A149761 A149762 A149763 * A149765 A149766 A149767

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved