Search: id:A016921
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%I A016921
%S A016921 1,7,13,19,25,31,37,43,49,55,61,67,73,79,85,91,97,103,109,115,121,127,
%T A016921 133,139,145,151,157,163,169,175,181,187,193,199,205,211,217,223,229,
%U A016921 235,241,247,253,259,265,271,277,283,289,295,301,307,313,319,325,331
%N A016921 6n+1.
%C A016921 Apart from initial term(s), dimension of the space of weight 2n cusp 
               forms for Gamma_0( 22 ).
%C A016921 Also solutions to 2^x+3^x == 5 mod 7. - Cino Hilliard (hillcino368(AT)gmail.com), 
               May 10 2003
%C A016921 Except for 1, exponents e such that x^e-x^2-1 is reducible.
%C A016921 Let M(n) be the n X n matrix m(i,j)=min(i,j) then the trace of M(n)^(-2) 
               is a(n-1)=6*n-5 - Benoit Cloitre (benoit7848c(AT)orange.fr), Feb 
               09 2006
%C A016921 If Y is a 3-subset of an (2n+1)-set X then, for n>=3, a(n-1) is the number 
               of 3-subsets of X having at least two elements in common with Y. 
               - Milan R. Janjic (agnus(AT)blic.net), Dec 16 2007
%C A016921 A008615(a(n)) = n. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Feb 27 2008
%C A016921 A157176(a(n)) = A013730(n). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Feb 24 2009]
%H A016921 <a href="Sindx_Rea.html#recLCC">Index entries for sequences related to 
               linear recurrences with constant coefficients</a>
%H A016921 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/
               RecursiveSequences.html">Recursive Sequences</a>
%H A016921 William A. Stein, <a href="http://modular.fas.harvard.edu/Tables/dimskg0n.gp">
               Dimensions of the spaces S_k(Gamma_0(N))</a>
%H A016921 William A. Stein, <a href="http://modular.fas.harvard.edu/Tables/">The 
               modular forms database</a>
%F A016921 G.f.: (1+5*x)/(1-x)^2.
%F A016921 a(n)=12*n-a(n-1)-16 (with a(1)=1) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), 
               Nov 27 2009]
%e A016921 For n=2, a(2)=12*2-1-16=7; n=3, a(3)=12*3-7-16=13; n=4, a(4)=12*4-13-16=19 
               [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 27 2009]
%p A016921 a[1]:=1:for n from 2 to 100 do a[n]:=a[n-1]+6 od: seq(a[n], n=1..56); 
               - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 16 2008
%t A016921 f[n_]:=6*n+1; lst={};Do[a=f[n];AppendTo[lst,a],{n,0,6!}];lst [From Vladimir 
               Orlovsky (4vladimir(AT)gmail.com), Jun 25 2009]
%o A016921 (Other) sage: [i+1 for i in range(333) if gcd(i,6) == 6] # [From Zerinvary 
               Lajos (zerinvarylajos(AT)yahoo.com), May 20 2009]
%Y A016921 Cf. A093563 ((6, 1) Pascal, column m=1). A000567 (partial sums).
%Y A016921 Cf. A008588, A016933, A016945, A016957, A016969.
%Y A016921 a(n)=A007310(2*(n+1)); complement of A016969 with respect to A007310. 
               [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Oct 02 
               2008]
%Y A016921 A161700, A005408, A016813, A017281, A017533, A158057, A161705, A161709, 
               A161714, A128470. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Jun 17 2009]
%Y A016921 Sequence in context: A059335 A070419 A080199 this_sequence A123843 A004082 
               A039281
%Y A016921 Adjacent sequences: A016918 A016919 A016920 this_sequence A016922 A016923 
               A016924
%K A016921 nonn,easy,new
%O A016921 0,2
%A A016921 N. J. A. Sloane (njas(AT)research.att.com).

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