A150816 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), (0, -1, 1), (0, 1, -1), (0, 1, 1), (1, 0, 1)}

1, 2, 8, 31, 136, 590, 2693, 12262, 57207, 266993, 1262974, 5981798, 28565047, 136604608, 656810502, 3162420406, 15283892129, 73959776962, 358882669335, 1743380069204, 8486712994924, 41353150789775, 201831466011484, 985908774276470, 4822318632528052, 23604571997644201, 115665780530706013

Offset

0,2

Links

Table of n, a(n) for n=0..26.

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, j, -1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[i, 1 + j, -1 + 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: A150813 A150814 A150815 * A150817 A150818 A009567

Adjacent sequences: A150813 A150814 A150815 * A150817 A150818 A150819

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved