

A150230


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), (0, 1, 1), (0, 0, 1), (1, 1, 0)}


0



1, 2, 6, 22, 80, 313, 1259, 5124, 21435, 90406, 385474, 1662597, 7209353, 31504664, 138446422, 611070712, 2710897905, 12068159661, 53915063043, 241675935311, 1086145539091, 4894892304188, 22111581168981, 100095906872247, 454080096326417, 2063622667969792, 9394806855443681, 42840971500111898
(list;
graph;
refs;
listen;
history;
text;
internal format)



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, 1 + j, k, 1 + n] + aux[i, j, 1 + k, 1 + n] + aux[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: A201372 A072547 A150229 * A191755 A150231 A150232
Adjacent sequences: A150227 A150228 A150229 * A150231 A150232 A150233


KEYWORD

nonn,walk


AUTHOR

Manuel Kauers, Nov 18 2008


STATUS

approved



