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 A081714 F(n)*L(n+1) where F=Fibonacci and L=Lucas numbers. 6
 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; text; internal format)
 OFFSET 0,2 COMMENTS Also convolution of Fibonacci and Lucas numbers. LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 FORMULA G.f.: x*(3-2*x)/((1+x)*(1-3*x+x^2)). a(n) = A122367(n)-(-1)^n. [R. J. Mathar, 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 a(n+1) = - A186679(2*n+1). [Reinhard Zumkeller, Feb 25 2011] 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); MATHEMATICA Fibonacci[Range[0, 50]]*LucasL[Range[0, 50]+1] (*From Vladimir Joseph Stephan Orlovsky, Mar 17 2011*) 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)) (MAGMA) [Fibonacci(n)*Lucas(n+1): n in [0..30]]; // Vincenzo Librandi, Sep 08 2012 CROSSREFS Cf. A000045, A000204. Sequence in context: A110565 A057433 A006074 * A117718 A176857 A086826 Adjacent sequences:  A081711 A081712 A081713 * A081715 A081716 A081717 KEYWORD nonn,easy AUTHOR Ralf Stephan, Apr 03 2003 EXTENSIONS Simpler definition from Michael Somos, Mar 16 2004 STATUS approved

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