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A222657 a(n) = 2 * floor( (2*n + 1) / 3) + 1.

%I A222657 #27 Sep 17 2024 18:00:58
%S A222657 1,3,3,5,7,7,9,11,11,13,15,15,17,19,19,21,23,23,25,27,27,29,31,31,33,
%T A222657 35,35,37,39,39,41,43,43,45,47,47,49,51,51,53,55,55,57,59,59,61,63,63,
%U A222657 65,67,67,69,71,71,73,75,75,77,79,79,81,83,83,85,87,87,89
%N A222657 a(n) = 2 * floor( (2*n + 1) / 3) + 1.
%C A222657 Dimension of the space of weight 2n+4 cusp forms for Gamma_0(7).
%H A222657 Harvey P. Dale, <a href="/A222657/b222657.txt">Table of n, a(n) for n = 0..1000</a>
%H A222657 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,1,-1).
%F A222657 G.f.: (1 + 2*x + x^3) / (1 - x - x^3 + x^4).
%F A222657 a(-n) = - A168056(n - 1).
%F A222657 a(n) = - A168053(n + 2).
%F A222657 a(n+3) = a(n) + 4.
%F A222657 a(n) = (12*n+9+4*sqrt(3)*sin(2*n*Pi/3))/9. - _Wesley Ivan Hurt_, Sep 29 2017
%e A222657 G.f. = 1 + 3*x + 3*x^2 + 5*x^3 + 7*x^4 + 7*x^5 + 9*x^6 + 11*x^7 + 11*x^8 + ...
%t A222657 Table[2Floor[(2n+1)/3]+1,{n,0,70}] (* or *) LinearRecurrence[{1,0,1,-1},{1,3,3,5},70] (* _Harvey P. Dale_, Sep 17 2024 *)
%o A222657 (PARI) {a(n) = (2*n + 1) \ 3 * 2 + 1};
%o A222657 (Sage) def a(n) : return( len( CuspForms( Gamma0( 7), 2*n + 4, prec=1). basis()));
%Y A222657 Cf. A168053, A168056.
%K A222657 nonn,easy
%O A222657 0,2
%A A222657 _Michael Somos_, May 29 2013