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A014335
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Exponential convolution of Fibonacci numbers with themselves (divided by 2).
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5
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0, 0, 1, 3, 11, 35, 115, 371, 1203, 3891, 12595, 40755, 131891, 426803, 1381171, 4469555, 14463795, 46805811, 151466803, 490156851, 1586180915, 5132989235, 16610702131, 53753361203, 173949530931
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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FORMULA
| G.f.: x^2/(1-2*x-4*x^2)/(1-x). - Vladeta Jovovic (vladeta(AT)eunet.rs), Mar 05 2003
E.g.f.: exp(x)*(cosh(sqrt(5)*x)-1)/5. - Vladeta Jovovic (vladeta(AT)eunet.rs), Sep 01 2004
a(n+1)=sum(i=0, n, F(i)*2^(i-1)); a(n)=(1/5)*(2^(n-1)*L(n)-1) where L(n) are Lucas numbers defined in A000032. - Benoit Cloitre (benoit7848c(AT)orange.fr), Sep 25 2004
a(n)=2*a(n-1)+4*a(n-2)+1, a(0)=0 ;a(1)=0 . [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 14 2008]
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MAPLE
| a[0]:=0:a[1]:=0:for n from 2 to 50 do a[n]:=2*a[n-1]+4*a[n-2]+1 od: seq(a[n], n=0..29); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 14 2008]
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MATHEMATICA
| Join[{a=0, b=0}, Table[c=2*b+4*a+1; a=b; b=c, {n, 60}]] (*From Vladimir Joseph Stephan Orlovsky, Feb 01 2011*)
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CROSSREFS
| Cf. (partial sums of) A063727, A081057, A014334.
Sequence in context: A034576 A125672 A107683 * A147474 A119143 A119092
Adjacent sequences: A014332 A014333 A014334 * A014336 A014337 A014338
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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