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%I #7 Jun 19 2016 22:35:12
%S 1,1,1,2,3,4,7,12,21,37,63,116,208,372,682,1255,2334,4277,7951,14905,
%T 27967,52334,98222,186344,352621,666933,1264406,2413511,4604124,
%U 8766995,16748492,32124034,61642942,118049157,226709069,436727197,841581933,1619406091
%N a(n) = total number of different ways a grasshopper can take n hops.
%C Consider a grasshopper (cf. A141000) that starts at x=0 at time 0, then makes successive hops of sizes 1, 2, 3, ..., n, subject to the constraint that it must always land on a point x >= 0; sequence gives number of different ways that it can make n hops.
%C Here, unlike A141000, there is no restriction on how large x can be (of course x <= n(n+1)/2).
%H David W. Wilson, <a href="/A141002/b141002.txt">Table of n, a(n) for n = 0..1000</a>
%e For example, for n=3 the grasshopper can hit 0=1+2-3 or 6=1+2+3; for n=4 it can hit 2=1+2+3-4, 4=1+2-3+4, or 10=1+2+3+4. For n=7 we can reach 8 in two different ways, which explains the first place where this sequence differs from A141001.
%Y Cf. A141000, A141001.
%K nonn
%O 0,4
%A _David Applegate_ and _N. J. A. Sloane_, Jul 21 2008
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