A150911 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, 0), (1, -1, -1), (1, 1, 0), (1, 1, 1)}.

1, 2, 9, 31, 145, 596, 2802, 12395, 58953, 269877, 1295133, 6050077, 29221939, 138340308, 671360915, 3208049603, 15624838414, 75174582036, 367173822737, 1775751859161, 8692898075676, 42212122305301, 207024738925159, 1008561691710785, 4953997096417660, 24198104921861654, 119014387562809316

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, -1 + k, -1 + n] + aux[-1 + i, -1 + j, k, -1 + n] + aux[-1 + i, 1 + j, 1 + k, -1 + n] + aux[1 + i, j, 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: A150908 A150909 A150910 * A150912 A165653 A182265

Adjacent sequences: A150908 A150909 A150910 * A150912 A150913 A150914

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved