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%I #30 Apr 17 2023 06:17:52
%S 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 15,15,16,17,16,18,18,18,19,20,19,21,21,21,22,23,22,24,24,24,25,26,25,
%U 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 a(n) = a(n-2) + a(n-3) - a(n-5).
%C a(n+6) = a(n) + 3; convolution of A000035(n) with A010872(n). - _Reinhard Zumkeller_, Mar 08 2009
%C 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 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 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,1,0,-1).
%F G.f.: x*(1+2*x)/((1-x^2)*(1-x^3)).
%F a(n) = Sum_{k=0..n} (k mod 3)*(1-(-1)^(n+k-1))/2}.
%F a(n) = Sum_{k=0..floor(n/2)} (n-2k mod 3).
%F a(n) = 1 + floor(n/2) - [3 divides n]. - _Ralf Stephan_, Nov 15 2010
%F a(n) = A103221(n-1) + 2*A103221(n-2). - _R. J. Mathar_, Jun 30 2011
%F a(n) = floor(n/2) + floor((n+2)/3) - floor(n/3). - _Mircea Merca_, May 20 2013
%o (PARI) a(n)=1+floor(n/2)-if(n%3==0,1,0)
%Y Cf. A174257. - _Vladimir Shevelev_, May 31 2011
%K easy,nonn
%O 0,3
%A _Paul Barry_, Apr 16 2005