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 A178982 Partial sums of floor(Fibonacci(n)/2). 2
 0, 0, 0, 1, 2, 4, 8, 14, 24, 41, 68, 112, 184, 300, 488, 793, 1286, 2084, 3376, 5466, 8848, 14321, 23176, 37504, 60688, 98200, 158896, 257105, 416010, 673124, 1089144, 1762278, 2851432, 4613721, 7465164, 12078896, 19544072, 31622980 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS Partial sums of A004695. LINKS Mircea Merca, Inequalities and Identities Involving Sums of Integer Functions J. Integer Sequences, Vol. 14 (2011), Article 11.9.1. FORMULA a(n) = round(Fibonacci(n+2)/2 - (n+2)/3). a(n) = round(Fibonacci(n+2)/2 - n/3 - 1/2). a(n) = floor(Fibonacci(n+2)/2 - n/3 - 1/2). a(n) = ceiling(Fibonacci(n+2)/2 - (n+1)/3 - 1/2). a(n) = a(n-3) + Fibonacci(n) - 1, n > 3. a(n) = 2*a(n-1) - 2*a(n-4) + a(n-6), n > 5. G.f.: -x^3 / ( (x^2+x+1)*(x^2+x-1)*(x-1)^2 ). a(n) = (1/2) * (Fibonacci(n+2) + floor(n/3) - n - 1). - Ralf Stephan, Jan 19 2014 EXAMPLE a(4) = 0 + 0 + 0 + 1 + 1 = 2. MAPLE seq(round(fibonacci(n+2)/2-(n+2)/3), n=0..40). MATHEMATICA f[n_] := Floor[Fibonacci@n/2]; Accumulate@ Array[f, 38, 0] CROSSREFS Cf. A004695, A164397. Sequence in context: A164168 A182747 A164406 * A164397 A164174 A164396 Adjacent sequences:  A178979 A178980 A178981 * A178983 A178984 A178985 KEYWORD nonn AUTHOR Mircea Merca, Jan 02 2011 STATUS approved

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Last modified July 26 02:10 EDT 2021. Contains 346294 sequences. (Running on oeis4.)