A148472 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, 0), (-1, 0, 1), (0, 1, 0), (1, -1, 1), (1, 0, -1)}.

1, 1, 2, 6, 19, 69, 259, 995, 3984, 16246, 67846, 288622, 1242949, 5426505, 23918477, 106383490, 477100523, 2153840179, 9786732365, 44713258872, 205300573048, 946979887510, 4385632308942, 20387463346828, 95097247477114, 444963582043322, 2088037680188809, 9824186906449215, 46336721367973800

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, j, 1 + k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[1 + i, j, -1 + k, -1 + n] + aux[1 + i, 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: A150105 A150106 A150107 * A150108 A150109 A150110

Adjacent sequences: A148469 A148470 A148471 * A148473 A148474 A148475

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved