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 A190062 a(n) = n*Fibonacci(n) - Sum_{i=0..n-1} Fibonacci(i). 5
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS Bruno Berselli, Table of n, a(n) for n = 0..1000 Carlos Alirio Rico Acevedo, Ana Paula Chaves, Double-Recurrence Fibonacci Numbers and Generalizations, arXiv:1903.07490 [math.NT], 2019. Index entries for linear recurrences with constant coefficients, signature (3,-1,-3,1,1). FORMULA G.f.: x*(1-2*x+2*x^2)/((1-x)*(1-x-x^2)^2). a(n) = A045925(n) - A000071(n+1). 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). MATHEMATICA 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 *) PROG (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 CROSSREFS Cf. A122491, A045925, A000071. Sequence in context: A056309 A007784 A008204 * A228231 A175657 A080287 Adjacent sequences: A190059 A190060 A190061 * A190063 A190064 A190065 KEYWORD nonn,easy AUTHOR Bruno Berselli, May 04 2011 STATUS approved

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Last modified May 28 21:07 EDT 2023. Contains 363028 sequences. (Running on oeis4.)