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A049651
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a(n)=(F(3n+1)-1)/2, where F=A000045 (the Fibonacci sequence).
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1
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0, 1, 6, 27, 116, 493, 2090, 8855, 37512, 158905, 673134, 2851443, 12078908, 51167077, 216747218, 918155951, 3889371024, 16475640049, 69791931222, 295643364939, 1252365390980, 5305104928861, 22472785106426
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| This is the sequence A(0,1;4,1;2)of the family of sequences [a,b:c,d:k] considered by G. Detlefs, and treated as A(a,b;c,d;k) in the W. Lang link given below. [From Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Oct 18 2010]
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REFERENCES
| A. T. Benjamin and J. J. Quinn, Proofs that really count: the art of combinatorial proof, M.A.A. 2003, id. 24.
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LINKS
| W. Lang, Notes on certain inhomogeneous three term recurrences. [From Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Oct 18 2010]
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FORMULA
| a(n)=4*a(n-1)+a(n-2)+2, a(0)=0, a(1)=1. G.f.: x*(x+1)/((x-1)*(x^2+4*x-1)). a(n) is asymptotic to -1/2+(sqrt(5)+5)/20*(sqrt(5)+2)^n. - Ralf Stephan (ralf(AT)ark.in-berlin.de), Jan 23 2003
a(n+1) = F(2) + F(5) + F(8) + ... + F(3n+2).
a(n) = 5*a(n-1) -3*a(n-2) - a(n-3), a(0)=0, a(1)=1, a(2)= 6. Observation by G. Detlefs. See the W. Lang link. [From Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Oct 18 2010]
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MATHEMATICA
| (Fibonacci[Range[1, 5!, 3]]-1)/2 [From Vladimir Orlovsky (4vladimir(AT)gmail.com), May 18 2010]
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CROSSREFS
| Cf. A033887.
Pairwise sums of A049652.
Sequence in context: A171475 A130019 A196919 * A109114 A080619 A080620
Adjacent sequences: A049648 A049649 A049650 * A049652 A049653 A049654
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KEYWORD
| nonn
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AUTHOR
| Clark Kimberling (ck6(AT)evansville.edu)
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