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Search: id:A084058
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| A084058 |
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a(n)=2a(n-1)+7a(n-2), a(0)=1, a(1)=1. |
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+0
7
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| 1, 1, 9, 25, 113, 401, 1593, 5993, 23137, 88225, 338409, 1294393, 4957649, 18976049, 72655641, 278143625, 1064876737, 4076758849, 15607654857, 59752621657, 228758827313, 875786006225, 3352883803641, 12836269650857, 49142725927201
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Binomial transform of expansion of cosh(sqrt(8)x) (A001018 with interpolated zeros : 1, 0, 8, 0, 64, 0, 512, 0, ...); inverse binomial transform of A084128.
The same sequence may be obtained by the following process. Starting a priori with the fraction 1/1, the numerators of fractions built according to the rule: add top and bottom to get the new bottom, add top and 8 times the bottom to get the new top. The limit of the sequence of fractions is sqrt(8). - Cino Hilliard (hillcino368(AT)gmail.com), Sep 25 2005
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REFERENCES
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John Derbyshire, Prime Obsession, Joseph Henry Press, April 2004, see p. 16.
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FORMULA
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a(n)=(1+sqrt(8))^n/2+(1-sqrt(8))^n/2; G.f.: (1-x)/(1-2x-7x^2); E.g.f.: exp(x)cosh(sqrt(8)x).
a(n)=Sum_{k, 0<=k<=n}A098158(n,k)*8^(n-k). - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Dec 26 2007
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CROSSREFS
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Essentially a duplicate of A083100.
Sequence in context: A075064 A083672 A083100 this_sequence A108570 A092769 A139818
Adjacent sequences: A084055 A084056 A084057 this_sequence A084059 A084060 A084061
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KEYWORD
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easy,nonn
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), May 10 2003
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