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A109454
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Sum of non-Fibonacci numbers between successive Fibonacci numbers: a(n) = Sum_{k=F(n)+1..F(n+1)-1} k.
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1
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0, 0, 0, 0, 4, 13, 42, 119, 330, 890, 2376, 6291, 16588, 43615, 114492, 300236, 786828, 2061233, 5398470, 14136759, 37015990, 96917974, 253748880, 664346375, 1739318904, 4553656703, 11921726232, 31211643384, 81713400340, 213928875445, 560073740226
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OFFSET
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0,5
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LINKS
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FORMULA
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a(n) = Fibonacci(n+2)*(Fibonacci(n-1)-1)/2, n>1. - Vladeta Jovovic, Aug 27 2005
a(n) = 3*a(n-1) + a(n-2) - 5*a(n-3) - a(n-4) + a(n-5) for n>6. - Colin Barker, Mar 26 2015
G.f.: x^4*(x^2-x-4) / ((x+1)*(x^2-3*x+1)*(x^2+x-1)). - Colin Barker, Mar 26 2015
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EXAMPLE
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F(5) = F(4) + 1 = 4.
F(6) = (F(5) + 1) + (F(5) + 2) = 6+7 = 13.
F(7) = 9+10+11+12 = 42.
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MATHEMATICA
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CoefficientList[Series[x^4*(x^2 - x - 4)/((x + 1) (x^2 - 3 x + 1) (x^2 + x - 1)), {x, 0, 30}], x] (* Michael De Vlieger, Jul 08 2021 *)
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PROG
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(PARI) concat([0, 0, 0, 0], Vec(x^4*(x^2-x-4) / ((x+1)*(x^2-3*x+1)*(x^2+x-1)) + O(x^100))) \\ Colin Barker, Mar 26 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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EXTENSIONS
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STATUS
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approved
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