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A190173
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a(n) = Sum_{1 <= i < j <= n} F(i)*F(j), where F(k) is the k-th Fibonacci number.
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11
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0, 1, 5, 17, 52, 148, 408, 1101, 2937, 7777, 20504, 53912, 141520, 371113, 972573, 2547825, 6672876, 17473996, 45754280, 119797205, 313650865, 821177281, 2149916400, 5628629232, 14736064032, 38579712913, 101003317493, 264430632401, 692289215332, 1812438042052
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OFFSET
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1,3
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LINKS
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FORMULA
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a(n) = F(n+1)^2 - F(n+2) + (1-(-1)^n)/2.
G.f.: x^2*(1+x-x^2)/((1-x)*(1+x)*(1-x-x^2)*(1-3*x+x^2)). - Bruno Berselli, Jun 20 2012
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EXAMPLE
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a(4) = F(1)*F(2) + F(1)*F(3) + F(1)*F(4) + F(2)*F(3) + F(2)*F(4) + F(3)*F(4) = 1 + 2 + 3 + 2 + 3 + 6 = 17.
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MAPLE
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with(combinat): seq(fibonacci(n+1)^2-fibonacci(n+2)+1/2-(1/2)*(-1)^n, n = 1 .. 30);
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MATHEMATICA
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Table[Fibonacci[n + 1]^2 - Fibonacci[n + 1] + (1 - (-1)^n)/2, {n, 1, 50}] (* G. C. Greubel, Mar 04 2017 *)
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PROG
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(Magma) [Fibonacci(n+1)^2 - Fibonacci(n+2) + (1-(-1)^n)/2: n in [1..30]]; // Vincenzo Librandi, Jun 05 2011
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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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