A151035 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, -1), (0, 0, 1), (0, 1, 0), (1, 0, 0)}.

1, 3, 9, 31, 117, 451, 1795, 7371, 30641, 129237, 553453, 2388067, 10391067, 45620153, 201301879, 893149801, 3986101427, 17854332707, 80282749777, 362491091255, 1641167116689, 7451783900471, 33939120865581, 154903175043917, 708578205070791, 3248944338251951, 14922213025784075, 68658552076475083

Offset

0,2

Links

Table of n, a(n) for n=0..27.

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, k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, 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: A110136 A202180 A151034 * A151036 A073724 A375453

Adjacent sequences: A151032 A151033 A151034 * A151036 A151037 A151038

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved