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 A179018 #27 Jul 04 2019 03:43:11 %S A179018 0,1,2,3,5,8,12,19,30,47,75,120,192,309,498,803,1297,2096,3388,5479, %T A179018 8862,14335,23191,37520,60704,98217,158914,257123,416029,673144, %U A179018 1089164 %N A179018 Partial sums of ceiling(Fibonacci(n)/2). %C A179018 Partial sums of A173173. %H A179018 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. %H A179018 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,0,-2,0,1). %F A179018 a(n) = round(Fibonacci(n+2)/2 + (n-1)/3). %F A179018 a(n) = round(Fibonacci(n+2)/2 + n/3 - 1/2). %F A179018 a(n) = floor(Fibonacci(n+2)/2 + n/3 - 1/6). %F A179018 a(n) = ceiling(Fibonacci(n+2)/2 + n/3 - 1/2). %F A179018 a(n) = a(n-3) + Fibonacci(n)+1, n > 2. %F A179018 a(n) = 2*a(n-1) - 2*a(n-4) + a(n-6), n > 5. %F A179018 G.f.: x*(x^3+x^2-1) / ( (x^2+x+1)*(x^2+x-1)*(x-1)^2 ). %e A179018 a(4) = 0 + 1 + 1 + 1 + 2 = 5. %p A179018 seq(ceil(Fibonacci(n+2)/2+n/3-1/2),n=0..30) %o A179018 (PARI) a(n)=(3*fibonacci(n+2)+2*n-1)\6 \\ _Charles R Greathouse IV_, Nov 02 2015 %Y A179018 Cf. A173173. %K A179018 nonn,easy %O A179018 0,3 %A A179018 _Mircea Merca_, Jan 04 2011