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A103433
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Sum[i=1..n, Fibonacci(2i-1)^2 ].
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5
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0, 1, 5, 30, 199, 1355, 9276, 63565, 435665, 2986074, 20466835, 140281751, 961505400, 6590256025, 45170286749, 309601751190, 2122041971551, 14544692049635, 99690802375860, 683290924581349, 4683345669693545
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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REFERENCES
| A. T. Benjamin and J. J. Quinn, Proofs that really count: the art of combinatorial proof, M.A.A. 2003, id. 234.
Michael Dougherty, Christopher French, Benjamin Saderholm, and Wenyang Qian, Hankel Transforms of Linear Combinations of Catalan Numbers, Journal of Integer Sequences, Vol. 14 (2011), Article 11.5.1
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (9,-16,9,-1).
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FORMULA
| G.f.: x(1-4x+x^2) / ((1-7x+x^2)(1-x)^2).
a(n)=(1/5)*( Fibonacci(4n) + 2n ).
a(n)=(floor(5*n*phi)+4*Fibonacci(4*n))/20, where phi =(1+sqrt(5))/2. [From Gary Detlefs (gdetlefs(AT)aol.com), Mar 10 2011]
a(n)= (8*(n+2)*sum(1/(2*k^2+6*k+4),k=1..n)+Fibonacci(4*n))/5. [From Gary Detlefs, Dec 07 2011]
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PROG
| (MAGMA) [(1/5)*(Fibonacci(4*n)+2*n): n in [0..50]]; // Vincenzo Librandi, Apr 20 2011
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CROSSREFS
| Partial sums of A081068. Bisection of A077916.
Sequence in context: A158828 A196471 A034164 * A081015 A090139 A107265
Adjacent sequences: A103430 A103431 A103432 * A103434 A103435 A103436
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KEYWORD
| nonn,easy
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AUTHOR
| Ralf Stephan, Feb 08 2005
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