A149879 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, 1), (0, 1, -1), (1, 0, 0), (1, 0, 1)}.

1, 2, 5, 14, 43, 138, 463, 1594, 5581, 19911, 71981, 262588, 967726, 3594012, 13422262, 50438467, 190475843, 722002522, 2747973433, 10494228944, 40182701649, 154300910627, 593948874999, 2290770087765, 8853590694541, 34280009601977, 132927197195087, 516262108031273, 2007836438965673

Offset

0,2

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, j, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, 1 + 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: A071751 A052301 A071755 * A366025 A366042 A149880

Adjacent sequences: A149876 A149877 A149878 * A149880 A149881 A149882

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved