

A150421


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


0



1, 2, 7, 24, 95, 381, 1620, 6952, 30527, 135709, 611338, 2780105, 12737432, 58751582, 272577928, 1271185910, 5954217923, 27994989600, 132078328817, 625071178375, 2966491655428, 14113589173293, 67299639843727, 321581250955477, 1539569388429159, 7383627382685730, 35468227398650854, 170630590833547054
(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, j, 1 + k, 1 + n] + aux[1 + i, j, 1 + k, 1 + n] + aux[i, j, 1 + k, 1 + n] + aux[1 + i, 1 + 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: A150418 A150419 A150420 * A150422 A137952 A005754
Adjacent sequences: A150418 A150419 A150420 * A150422 A150423 A150424


KEYWORD

nonn,walk


AUTHOR

Manuel Kauers, Nov 18 2008


STATUS

approved



