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A081714
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F(n)L(n+1) where F=Fibonacci and L=Lucas numbers.
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5
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0, 3, 4, 14, 33, 90, 232, 611, 1596, 4182, 10945, 28658, 75024, 196419, 514228, 1346270, 3524577, 9227466, 24157816, 63245987, 165580140, 433494438, 1134903169, 2971215074, 7778742048, 20365011075, 53316291172
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Also convolution of Fibonacci and Lucas numbers.
a(n+1) = - A186679(2*n+1). [Reinhard Zumkeller, Feb 25 2011]
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FORMULA
| G.f.: x(3-2x)/((1+x)(1-3x+x^2)).
a(n) = A122367(n)-(-1)^n. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 23 2010]
a(n)= (L(n+1)^2-F(2*n+2))/2 = ( A001254(n+1)-A001906(n+1) )/2 - Gary Detlefs, Nov 28 2010
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MAPLE
| with(combinat):F:=n-> fibonacci(n):L:=n->2*F(n+1)+F(n):
seq(1/2*(L(n+1)^2-F(2*n+2), n=0..26);
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MATHEMATICA
| Fibonacci[Range[0, 50]]*LucasL[Range[0, 50]+1] (*From Vladimir Joseph Stephan Orlovsky, Mar 17 2011*)
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PROG
| (PARI) for(n=0, 50, print1(polcoeff(serconvol(Ser((1+2*x)/(1-x-x*x)), Ser(x/(1-x-x*x))), n)", "))
(PARI) a(n)=fibonacci(n)*(fibonacci(n+2)+fibonacci(n))
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CROSSREFS
| Cf. A000045, A000204.
Sequence in context: A110565 A057433 A006074 * A117718 A176857 A086826
Adjacent sequences: A081711 A081712 A081713 * A081715 A081716 A081717
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KEYWORD
| nonn,easy
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AUTHOR
| Ralf Stephan (ralf(AT)ark.in-berlin.de), Apr 03 2003
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EXTENSIONS
| Simpler definition from Michael Somos, Mar 16 2004
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