A150810 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), (0, -1, 1), (0, 1, -1), (0, 1, 1), (1, 0, 1)}

1, 2, 8, 31, 134, 584, 2642, 12055, 55981, 261467, 1233884, 5845271, 27878434, 133328052, 640637869, 3084629751, 14902927109, 72118713781, 349894102528, 1699796687804, 8274096040091, 40319508029331, 196787170415789, 961331747585813, 4702270029715186, 23018547284046684, 112799959775131455

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, 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: A150807 A150808 A150809 * A150811 A150812 A150813

Adjacent sequences: A150807 A150808 A150809 * A150811 A150812 A150813

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved