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 A109454 Sum of non-Fibonacci numbers between successive Fibonacci numbers: a(n) = Sum_{k=F(n)+1..F(n+1)-1)} k. 1
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 LINKS Colin Barker, Table of n, a(n) for n = 0..1000 Paul Barry, On the Gap-sum and Gap-product Sequences of Integer Sequences, arXiv:2104.05593 [math.CO], 2021. Index entries for linear recurrences with constant coefficients, signature (3,1,-5,-1,1). FORMULA 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 EXAMPLE F(5) = F(4) + 1 = 4. F(6) = (F(5) + 1) + (F(5) + 2) = 6+7 = 13. F(7) = 9+10+11+12 = 42. MAPLE with(combinat): P:=proc(n) ((fibonacci(n+1)-1)*fibonacci(n+1)-fibonacci(n)*(fibonacci(n)+1))/2; end: [0, 0, seq(P(i), i=2..30)]; # Paolo P. Lava, Apr 27 2018 MATHEMATICA 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 *) PROG (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 CROSSREFS Cf. A000045, A006002. Sequence in context: A036366 A303863 A255836 * A307261 A287349 A000640 Adjacent sequences:  A109451 A109452 A109453 * A109455 A109456 A109457 KEYWORD nonn,easy AUTHOR Amarnath Murthy, Aug 27 2005 EXTENSIONS More terms from Franklin T. Adams-Watters, Jun 06 2006 STATUS approved

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Last modified August 2 13:35 EDT 2021. Contains 346424 sequences. (Running on oeis4.)