A148835 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, 0), (0, 0, -1), (0, 1, 1), (1, -1, 1)}.

1, 1, 3, 8, 27, 90, 314, 1128, 4125, 15617, 59436, 230199, 899121, 3548174, 14149729, 56737430, 229465613, 932484468, 3812198941, 15663469773, 64627311946, 267921946059, 1114424402846, 4653403556951, 19491961759130, 81895933263661, 345122030631641, 1458040592790025, 6176186619051630

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, -1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[1 + i, 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: A145967 A145792 A148834 * A148836 A148837 A148838

Adjacent sequences: A148832 A148833 A148834 * A148836 A148837 A148838

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved