A148971 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, -1)}

1, 1, 3, 9, 32, 102, 396, 1454, 5877, 22415, 93613, 373105, 1590574, 6494352, 28142556, 117343359, 514812790, 2179682962, 9658749443, 41415470371, 185020861727, 801523426999, 3605125998161, 15752685563124, 71260738011618, 313653410879026, 1425875494127417, 6315416792853604, 28832664863417811

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[-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: A039749 A034538 A034540 * A148972 A148973 A148974

Adjacent sequences: A148968 A148969 A148970 * A148972 A148973 A148974

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved