%I A130206
%S A130206 1,2,3,5,7,9,12,15,18,22,26,30,35,40,45,51,57,63,70,77,84,92,100,108,
%T A130206 117,126,135,145,155,165,176,187,198,210,222,234,247,260,273,287,301,
%U A130206 315,330,345,360,376,392,408,425,442,459,477,495,513,532,551,570,590
%N A130206 a(1) = 1, a(2) = 2; for n>2, a(n) = t(n)-a(n-1)-a(n-2), where t(n) = 
               n(n+1)/2 = triangular number A000217.
%C A130206 Any three consecutive terms sum up to a triangular number. Essentially 
               A001840.
%F A130206 G.f.: x/(1+x+x^2)/(1-x)^3 [From Maksym Voznyy (voznyy(AT)mail.ru), Jul 
               27 2009]
%F A130206 a(n) = (4+3*n^2+9*n)/18+((n mod 3)-((n-1) mod 3))/9. [From Klaus Brockhaus 
               (klaus-brockhaus(AT)t-online.de), Oct 01 2009]
%F A130206 a(n) = a(n-1)+a(n-3)-a(n-4)+1 for n > 4; a(1)=1, a(2)=2, a(3)=3, a(4)=5. 
               [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Oct 04 2009]
%F A130206 a(n) = a(n-1)+a(n-3)-a(n-4)+1 for n > 4; a(1)=1, a(2)=2, a(3)=3, a(4)=5. 
               [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Oct 15 2009]
%e A130206 1+2+3=6=t(3), 2+3+5=t(4), 5+7+9=t(5).
%t A130206 a[1]=1;a[2]=2;a[n_]:=a[n]=n(n+1)/2-a[n-1]-a[n-2]; Table[a[n],{n,100}]
%o A130206 (MAGMA) [ n le 2 select n else n*(n+1)/2-Self(n-1)-Self(n-2): n in [1..58] 
               ]; [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Oct 01 
               2009]
%o A130206 (Other) sage: [floor(binomial(n,2)/3) for n in xrange(3,61)]# [From Zerinvary 
               Lajos (zerinvarylajos(AT)yahoo.com), Dec 01 2009]
%Y A130206 Cf. A000217, A001840, A130205.
%Y A130206 Sequence in context: A058937 A130518 A001840 this_sequence A022794 A025693 
               A117930
%Y A130206 Adjacent sequences: A130203 A130204 A130205 this_sequence A130207 A130208 
               A130209
%K A130206 nonn,new
%O A130206 1,2
%A A130206 Zak Seidov (zakseidov(AT)yahoo.com), May 16 2007
%E A130206 G.f. proposed by Maksym Voznyy checked and corrected by R. J. Mathar, 
               Sep 16 2009.