A149453 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, 1), (-1, 1, 0), (0, -1, 1), (1, 0, -1), (1, 1, 0)}

1, 1, 4, 13, 49, 197, 812, 3474, 15158, 67376, 303459, 1383358, 6363572, 29509269, 137771543, 646907907, 3052952032, 14470721920, 68854163470, 328735177885, 1574256833505, 7559227173640, 36385912226315, 175525189436472, 848409828992201, 4108222390467437, 19925762711434817, 96789429703804583

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, k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + j, k, -1 + n] + aux[1 + i, j, -1 + 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: A149451 A149452 A140660 * A149454 A101125 A284336

Adjacent sequences: A149450 A149451 A149452 * A149454 A149455 A149456

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved