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A141002
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a(n) = total number of different ways a grasshopper can take n hops.
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1
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1, 1, 1, 2, 3, 4, 7, 12, 21, 37, 63, 116, 208, 372, 682, 1255, 2334, 4277, 7951, 14905, 27967, 52334, 98222, 186344, 352621, 666933, 1264406, 2413511, 4604124, 8766995, 16748492, 32124034, 61642942, 118049157, 226709069, 436727197, 841581933, 1619406091
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| 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.
Here, unlike A141000, there is no restriction on how large x can be (of course x <= n(n+1)/2).
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EXAMPLE
| 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.
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CROSSREFS
| Cf. A141000, A141001.
Sequence in context: A073147 A018148 A084972 * A006537 A103963 A006706
Adjacent sequences: A140999 A141000 A141001 * A141003 A141004 A141005
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KEYWORD
| nonn
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AUTHOR
| David Applegate and N. J. A. Sloane (njas(AT)research.att.com), Jul 21 2008
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