A149093 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, 1), (-1, 0, 0), (1, 0, -1), (1, 1, 0)}.

1, 1, 4, 8, 32, 84, 346, 1035, 4398, 14222, 61684, 210612, 926902, 3292765, 14655294, 53664171, 240961436, 903803156, 4087224128, 15633002424, 71112783970, 276447837298, 1263743381144, 4980630942098, 22864035964645, 91177566889046, 420076191695644, 1692376534197673, 7821793195702664

Offset

0,3

Links

Table of n, a(n) for n=0..28.

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[-1 + i, j, 1 + k, -1 + n] + aux[1 + i, j, k, -1 + n] + aux[1 + i, 1 + 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: A358046 A094015 A094867 * A149094 A086344 A209084

Adjacent sequences: A149090 A149091 A149092 * A149094 A149095 A149096

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved