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 A049681 a(n) = (L(2*n) - L(n))/2, where L=A000032 (the Lucas sequence). 2
 0, 1, 2, 7, 20, 56, 152, 407, 1080, 2851, 7502, 19702, 51680, 135461, 354902, 929567, 2434320, 6374236, 16689752, 43697227, 114405500, 299525051, 784179002, 2053027082, 5374926720, 14071792681 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Create a triangle with T(n,1)=L(n-1) for L a Lucas number and the other side T(n,n)=L(2*(n-1)).  Interior elements are defined as T(r,c)=T(r-1,c-1)+T(r-1,c).  Half the sum of the terms in row(n)=a(n) for n=1,2,3...- J. M. Bergot, Dec 15 2012 LINKS Robert Israel, Table of n, a(n) for n = 0..2380 Index entries for linear recurrences with constant coefficients, signature (4,-3,-2,1). FORMULA G.f.: -x*(1-2*x+2*x^2)/( (x^2+x-1)*(x^2-3*x+1) ). - R. J. Mathar, Dec 17 2012 a(n) = Lucas(n)*(Lucas(n) - 1)/2 - (-1)^n = binomial(Lucas(n), 2) - (-1)^n. - Vladimir Reshetnikov, Sep 27 2016 MAPLE Lucas:= n -> combinat:-fibonacci(n+1)+combinat:-fibonacci(n-1): seq((Lucas(2*n)-Lucas(n))/2, n=0..100); # Robert Israel, Sep 15 2016 MATHEMATICA Table[(LucasL[2n] - LucasL[n])/2, {n, 0, 20}] (* Vladimir Reshetnikov, Sep 15 2016 *) PROG (PARI) x='x+O('x^30); concat([0], Vec(-x*(1-2*x+2*x^2)/( (x^2+x-1)*(x^2-3*x+1) ))) \\ G. C. Greubel, Dec 02 2017 (MAGMA) [(Lucas(2*n) - Lucas(n))/2: n in [0..30]]; // G. C. Greubel, Dec 02 2017 CROSSREFS Cf. A094292. Sequence in context: A018033 A000149 A080041 * A027120 A094982 A292400 Adjacent sequences:  A049678 A049679 A049680 * A049682 A049683 A049684 KEYWORD nonn AUTHOR EXTENSIONS Corrected by Franklin T. Adams-Watters, Oct 25 2006 Corrected by T. D. Noe, Nov 01 2006 STATUS approved

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Last modified April 19 20:04 EDT 2019. Contains 322291 sequences. (Running on oeis4.)