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A106729
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Sum of two consecutive squares of Lucas numbers (A001254).
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5
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5, 10, 25, 65, 170, 445, 1165, 3050, 7985, 20905, 54730, 143285, 375125, 982090, 2571145, 6731345, 17622890, 46137325, 120789085, 316229930, 827900705, 2167472185, 5674515850, 14856075365, 38893710245, 101825055370, 266581455865
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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LINKS
| Bruno Berselli, Table of n, a(n) for n = 0..300
Index entries for sequences related to linear recurrences with constant coefficients, signature (3,-1).
Tanya Khovanova, Recursive Sequences
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FORMULA
| a(n) = L(n)^2 + L(n+1)^2 = 5*(F(n)^2 + F(n+1)^2) = 5*A001519(n+1).
a(n) = 3*a(n-1)-a(n-2) - T. D. Noe, Dec 11 2006
G.f.: 5*(1-x)/(1-3*x+x^2) - Philippe DELEHAM, Nov 16 2008
a(n) = (5/2)*((3/2)+(1/2)*sqrt(5))^n+(1/2)*((3/2)+(1/2)*sqrt(5))^n*sqrt(5)-(1/2)*((3/2)-(1/2)*sqrt(5))^n *sqrt(5)+(5/2)*((3/2)-(1/2)*sqrt(5))^n, with n>=0 - Paolo P. Lava, Nov 19 2008
a(n) = Fibonacci(n-2)^2+Fibonacci(n+3)^2 - Gary Detlefs, Dec 28 2010
For n>=3, a(n)=[1,1;1,2]^(n-2).{3,4}.{3,4} - John M. Campbell, Jul 09 2011
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PROG
| (MAGMA) [Fibonacci(n-2)^2+Fibonacci(n+3)^2: n in [0..30]]; // Vincenzo Librandi, Jul 09 2011
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CROSSREFS
| Cf. A000204.
Sequence in context: A045620 A025625 A112024 * A038252 A083010 A166388
Adjacent sequences: A106726 A106727 A106728 * A106730 A106731 A106732
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KEYWORD
| nonn,easy
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AUTHOR
| Lekraj Beedassy (blekraj(AT)yahoo.com), May 14 2005
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EXTENSIONS
| Corrected by T. D. Noe (noe(AT)sspectra.com), Dec 11 2006
More terms by Bruno Berselli, Jul 17 2011
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