This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A178982 #30 Jul 04 2019 03:39:04 %S A178982 0,0,0,1,2,4,8,14,24,41,68,112,184,300,488,793,1286,2084,3376,5466, %T A178982 8848,14321,23176,37504,60688,98200,158896,257105,416010,673124, %U A178982 1089144,1762278,2851432,4613721,7465164,12078896,19544072,31622980 %N A178982 Partial sums of floor(Fibonacci(n)/2). %C A178982 Partial sums of A004695. %H A178982 Mircea Merca, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL14/Merca/merca3.html">Inequalities and Identities Involving Sums of Integer Functions</a> J. Integer Sequences, Vol. 14 (2011), Article 11.9.1. %F A178982 a(n) = round(Fibonacci(n+2)/2 - (n+2)/3). %F A178982 a(n) = round(Fibonacci(n+2)/2 - n/3 - 1/2). %F A178982 a(n) = floor(Fibonacci(n+2)/2 - n/3 - 1/2). %F A178982 a(n) = ceiling(Fibonacci(n+2)/2 - (n+1)/3 - 1/2). %F A178982 a(n) = a(n-3) + Fibonacci(n) - 1, n > 3. %F A178982 a(n) = 2*a(n-1) - 2*a(n-4) + a(n-6), n > 5. %F A178982 G.f.: -x^3 / ( (x^2+x+1)*(x^2+x-1)*(x-1)^2 ). %F A178982 a(n) = (1/2) * (Fibonacci(n+2) + floor(n/3) - n - 1). - _Ralf Stephan_, Jan 19 2014 %e A178982 a(4) = 0 + 0 + 0 + 1 + 1 = 2. %p A178982 seq(round(fibonacci(n+2)/2-(n+2)/3),n=0..40). %t A178982 f[n_] := Floor[Fibonacci@n/2]; Accumulate@ Array[f, 38, 0] %Y A178982 Cf. A004695, A164397. %K A178982 nonn %O A178982 0,5 %A A178982 _Mircea Merca_, Jan 02 2011