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A215602
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a(n) = L(n)*L(n+1), where L = A000032 (Lucas numbers).
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4
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2, 3, 12, 28, 77, 198, 522, 1363, 3572, 9348, 24477, 64078, 167762, 439203, 1149852, 3010348, 7881197, 20633238, 54018522, 141422323, 370248452, 969323028, 2537720637, 6643838878, 17393796002, 45537549123, 119218851372, 312119004988, 817138163597, 2139295485798, 5600748293802, 14662949395603, 38388099893012, 100501350283428
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OFFSET
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0,1
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LINKS
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FORMULA
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G.f.: ( 2-x+2*x^2 ) / ( (1+x)*(x^2-3*x+1) ). - R. J. Mathar, Aug 21 2012
a(n) = F(n-1)*F(n) + F(n-1)*F(n+2) + F(n+1)*F(n) + F(n+1)*F(n+2), where F=A000045, F(-1)=1. - Bruno Berselli, Nov 03 2015
a(n) = ((-1)^n+(2^(-1-n)*((3-sqrt(5))^n*(-5+sqrt(5))+(3+sqrt(5))^n*(5+sqrt(5)))) / sqrt(5)). - Colin Barker, Oct 01 2016
Sum_{n>=0} (-1)^n/a(n) = sqrt(5)/10. - Amiram Eldar, Oct 06 2020
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MATHEMATICA
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Table[LucasL[n]*LucasL[n + 1], {n, 0, 33}] (* Amiram Eldar, Oct 06 2020 *)
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PROG
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(PARI) a(n) = round(((-1)^n+(2^(-1-n)*((3-sqrt(5))^n*(-5+sqrt(5))+(3+sqrt(5))^n*(5+sqrt(5))))/sqrt(5))) \\ Colin Barker, Oct 01 2016
(PARI) Vec((2-x+2*x^2)/((1+x)*(x^2-3*x+1)) + O(x^30)) \\ Colin Barker, Oct 01 2016
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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