%I A014209
%S A014209 1,3,9,17,27,39,53,69,87,107,129,153,179,207,237,269,303,
%T A014209 339,377,417,459,503,549,597,647,699,753,809,867,927,989,
%U A014209 1053,1119,1187,1257,1329,1403,1479,1557,1637,1719,1803
%V A014209 -1,3,9,17,27,39,53,69,87,107,129,153,179,207,237,269,303,
%W A014209 339,377,417,459,503,549,597,647,699,753,809,867,927,989,
%X A014209 1053,1119,1187,1257,1329,1403,1479,1557,1637,1719,1803
%N A014209 n^2+3*n-1.
%C A014209 Difference between n-th centered hexagonal number and (2n)^2. - Alonso 
               Delarte (alonso.delarte(AT)gmail.com), Jul 06 2004
%C A014209 Contribution from Gary W. Adamson (qntmpkt(AT)yahoo.com), Jul 29 2009: 
               (Start)
%C A014209 Given the roots to n^2 + 3n - 1, a = -3.302775..., b = .302775...; then
%C A014209 a(n) = (n + 3 + a) * (n + 3 + b). Example: a(3) = 17 = (6 - 3.302...) 
               *
%C A014209 (6 + .302775) (End)
%H A014209 Anonymous Collective, <a href="http://en.wikipedia.org/wiki/Centered_hexagonal_number">
               Centered Hexagonal Numbers</a>.
%F A014209 a(n)=2*n+a(n-1) (with a(1)=-1) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), 
               Nov 29 2009]
%e A014209 For n=2, a(2)=2*2-1=3; n=3, a(3)=2*3+3=9; n=4, a(4)=2*4+9=17 [From Vincenzo 
               Librandi (vincenzo.librandi(AT)tin.it), Nov 29 2009]
%p A014209 a:=n->sum(k,k=0..n):seq(a(n)+sum(k,k=3..n),n=1..42); - Zerinvary Lajos 
               (zerinvarylajos(AT)yahoo.com), Mar 27 2008
%p A014209 with (combinat):seq(fibonacci(3, n)+n-4, n=1..43); - Zerinvary Lajos 
               (zerinvarylajos(AT)yahoo.com), Jun 07 2008
%t A014209 f[n_]:=(n+5)*n-(n+(n+1)); lst={};Do[AppendTo[lst,f[n]],{n,0,5!}];lst 
               [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Oct 08 2009]
%Y A014209 Cf. A003215.
%Y A014209 Cf. A002522.
%Y A014209 Sequence in context: A103967 A032400 A004621 this_sequence A057258 A018466 
               A035107
%Y A014209 Adjacent sequences: A014206 A014207 A014208 this_sequence A014210 A014211 
               A014212
%K A014209 sign,new
%O A014209 0,2
%A A014209 N. J. A. Sloane (njas(AT)research.att.com).