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A190062
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a(n) = n*Fibonacci(n) - Sum_{i=0..n-1} Fibonacci(i).
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5
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0, 1, 1, 4, 8, 18, 36, 71, 135, 252, 462, 836, 1496, 2653, 4669, 8164, 14196, 24566, 42332, 72675, 124355, 212156, 360986, 612744, 1037808, 1754233, 2959801, 4985476, 8384480, 14080602, 23614932, 39556031, 66181311, 110608188, 184670694
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OFFSET
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0,4
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LINKS
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FORMULA
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G.f.: x*(1-2*x+2*x^2)/((1-x)*(1-x-x^2)^2).
a(n) = (n-1)*Fibonacci(n) - Fibonacci(n-1) + 1.
a(n) = (((2*n-1)*r-5)*(1+r)^n-((2*n-1)*r+5)*(1-r)^n)/(10*2^n)+1, where r=sqrt(5).
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MATHEMATICA
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CoefficientList[Series[x (1 - 2 x + 2 x^2) / ((1 - x) (1 - x - x^2)^2), {x, 0, 35}], x] (* Vincenzo Librandi, Aug 19 2013 *)
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PROG
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(Magma) [0] cat [n*Fibonacci(n)-(&+[Fibonacci(k): k in [0..n-1]]): n in [1..34]];
(PARI) concat(0, Vec(x*(1-2*x+2*x^2)/((1-x)*(1-x-x^2)^2) + O(x^50))) \\ Altug Alkan, Nov 13 2015
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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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