

A148786


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


0



1, 1, 3, 8, 24, 79, 277, 973, 3608, 13763, 52434, 206021, 823010, 3282418, 13350760, 54934079, 225590067, 939423614, 3945522784, 16537919855, 70055121216, 298712178611, 1271246883045, 5455314627402, 23533860254593, 101337197334830, 439327885074430, 1912875711096559, 8314329148357597
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OFFSET

0,3


LINKS

Table of n, a(n) for n=0..28.
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, j, 1 + k, 1 + n] + aux[i, j, 1 + k, 1 + n] + aux[1 + i, 1 + j, 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: A066350 A148784 A148785 * A215576 A088966 A242985
Adjacent sequences: A148783 A148784 A148785 * A148787 A148788 A148789


KEYWORD

nonn,walk


AUTHOR

Manuel Kauers, Nov 18 2008


STATUS

approved



