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 A105637 #40 Jan 18 2025 07:45:29
%S A105637 0,1,2,1,3,3,3,4,5,4,6,6,6,7,8,7,9,9,9,10,11,10,12,12,12,13,14,13,15,
%T A105637 15,15,16,17,16,18,18,18,19,20,19,21,21,21,22,23,22,24,24,24,25,26,25,
%U A105637 27,27,27,28,29,28,30,30,30,31,32,31,33,33,33,34,35,34,36,36,36,37,38,37
%N A105637 a(n) = a(n-2) + a(n-3) - a(n-5).
%C A105637 a(n+6) = a(n) + 3; convolution of A000035(n) with A010872(n). - _Reinhard Zumkeller_, Mar 08 2009
%C A105637 Let B be the periodic sequence that repeats (1,2,1,3,3,3,4,5,4,6,6,6). Then the sequence a(1), a(2), ... is obtained by adding 6*(i-1) to every term of the i-th period of B. - _Vladimir Shevelev_, May 31 2011
%C A105637 Also for n > 0: number of partitions of n into parts 1 or 2 with distinct multiplicities, cf. A211858, A098859. - _Reinhard Zumkeller_, Dec 27 2012
%H A105637 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,1,0,-1).
%F A105637 G.f.: x*(1+2*x)/((1-x^2)*(1-x^3)).
%F A105637 a(n) = Sum_{k=0..n} (k mod 3)*(1-(-1)^(n+k-1))/2.
%F A105637 a(n) = Sum_{k=0..floor(n/2)} (n-2k mod 3).
%F A105637 a(n) = 1 + floor(n/2) - [3 divides n]. - _Ralf Stephan_, Nov 15 2010
%F A105637 a(n) = A103221(n-1) + 2*A103221(n-2). - _R. J. Mathar_, Jun 30 2011
%F A105637 a(n) = floor(n/2) + floor((n+2)/3) - floor(n/3). - _Mircea Merca_, May 20 2013
%o A105637 (PARI) a(n)=1+floor(n/2)-if(n%3==0,1,0)
%Y A105637 Cf. A000035, A010872, A103221.
%K A105637 nonn,easy
%O A105637 0,3
%A A105637 _Paul Barry_, Apr 16 2005