A149592 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, 0, -1), (1, 1, 1)}

1, 1, 5, 15, 57, 217, 903, 3645, 15229, 65109, 279725, 1204423, 5273461, 23266449, 102770929, 456619979, 2044838287, 9174556253, 41260461173, 186519911601, 846046745543, 3842514321441, 17500036179883, 79949992917127, 365810233538901, 1676310128392741, 7700039803930915, 35433077447719615

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[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: A110614 A149590 A149591 * A149593 A230986 A149594

Adjacent sequences: A149589 A149590 A149591 * A149593 A149594 A149595

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved