A150769 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), (-1, 0, 1), (0, 0, -1), (1, 0, 1), (1, 1, 0)}

1, 2, 8, 30, 128, 549, 2450, 11046, 50673, 234383, 1094288, 5140068, 24286027, 115257393, 549211095, 2625763721, 12591106792, 60531714120, 291672527621, 1408264922792, 6811785194023, 33002323933080, 160128596210190, 777991490254078, 3784531914550388, 18430465713070713, 89847986852919897

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, -1 + j, k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[1 + i, 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: A150766 A150767 A150768 * A150770 A150771 A150772

Adjacent sequences: A150766 A150767 A150768 * A150770 A150771 A150772

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved