%I A109613
%S A109613 1,1,3,3,5,5,7,7,9,9,11,11,13,13,15,15,17,17,19,19,21,21,23,23,25,25,27,
%T A109613 27,29,29,31,31,33,33,35,35,37,37,39,39,41,41,43,43,45,45,47,47,49,49,
%U A109613 51,51,53,53,55,55,57,57,59,59,61,61,63,63,65,65,67,67,69,69,71,71,73
%N A109613 Odd numbers repeated.
%C A109613 a(n) = A052928(n) + 1 = 2*A004526(n) + 1.
%C A109613 a(n) = A028242(n) + A110654(n).
%C A109613 Diagonal sums of number triangle A113126. - Paul Barry (pbarry(AT)wit.ie), 
               Oct 14 2005
%C A109613 When partitioning a convex n-gon by all the diagonals, the maximum number 
               of sides in resulting polygons is 2*floor(n/2)+1 = a(n-1) (from Moscow 
               Olympiad problem 1950) - Tanya Khovanova (tanyakh(AT)yahoo.com), 
               Apr 06 2008
%C A109613 Its ordinal transform is A000034 [From Paolo P. Lava (ppl(AT)spl.at), 
               Jun 25 2009]
%C A109613 Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Nov 12 
               2009: (Start)
%C A109613 The inverse values of the coefficients in the series expansion of f(x) 
               = (1/2)*(1+x)*ln((1+x)/(1-x)) lead to this sequence; cf. A098557.
%C A109613 (End)
%C A109613 Contribution from Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Dec 05 2009: (Start)
%C A109613 First differences: A010673; partial sums: A000982;
%C A109613 A059329(n) = SUM(a(k)*a(n-k): 0<=k<=n);
%C A109613 A167875(n) = SUM(a(k)*A005408(n-k): 0<=k<=n);
%C A109613 A171218(n) = SUM(a(k)*A005843(n-k): 0<=k<=n);
%C A109613 A008794(n+2) = SUM(a(k)*A059841(n-k): 0<=k<=n). (End)
%F A109613 a(n) = 2*floor(n/2) + 1.
%F A109613 a(n) = A052938(n-2) + A084964(n-2) for n>1. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Aug 27 2005
%F A109613 G.f.: (1+x+x^2+x^3)/(1-x^2)^2; - Paul Barry (pbarry(AT)wit.ie), Oct 14 
               2005
%F A109613 a(n)=n+[1+(-1)^n]/2, with n>=0 - Paolo P. Lava (ppl(AT)spl.at), May 08 
               2007
%F A109613 a(n)=2*a(n-2)-a(n-4); a(0)=1, a(1)=1, a(2)=3, a(3)=3. [From Philippe 
               DELEHAM (kolotoko(AT)wanadoo.fr), Nov 03 2008]
%F A109613 a(n)=A001477(n)+A059841(n). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), 
               Mar 31 2009]
%F A109613 a(n)=2*n-a(n-1)-2 (with a(1)=1) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), 
               Nov 21 2009]
%e A109613 For n=2, a(2)=2*2-1-2=1; n=3, a(3)=2*3-1-2=3; n=4, a(4)=2*4-3-2=3 [From 
               Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 21 2009]
%Y A109613 Cf. A063196, A110660.
%Y A109613 Sequence in context: A117767 A063196 A127630 this_sequence A073737 A133908 
               A111213
%Y A109613 Adjacent sequences: A109610 A109611 A109612 this_sequence A109614 A109615 
               A109616
%K A109613 nonn,new
%O A109613 0,3
%A A109613 Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Aug 01 2005