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A047233 Numbers that are congruent to {0, 4} mod 6.

%I A047233 #67 Aug 26 2022 08:36:35
%S A047233 0,4,6,10,12,16,18,22,24,28,30,34,36,40,42,46,48,52,54,58,60,64,66,70,
%T A047233 72,76,78,82,84,88,90,94,96,100,102,106,108,112,114,118,120,124,126,
%U A047233 130,132,136,138,142,144,148,150,154,156,160,162,166,168,172,174,178,180,184,186,190,192,196,198
%N A047233 Numbers that are congruent to {0, 4} mod 6.
%C A047233 Apart from initial term(s), dimension of the space of weight 2*n cusp forms for Gamma_0(17).
%C A047233 Nonnegative k such that k*(k + 2)/6 is an integer. - _Bruno Berselli_, Mar 06 2018
%H A047233 Bruno Berselli, <a href="/A047233/b047233.txt">Table of n, a(n) for n = 1..10000</a>
%H A047233 William A. Stein, <a href="http://wstein.org/Tables/dimskg0n.gp">Dimensions of the spaces S_k(Gamma_0(N))</a>.
%H A047233 William A. Stein, <a href="http://wstein.org/Tables/">The modular forms database</a>.
%H A047233 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).
%F A047233 From _Bruno Berselli_, Jun 24 2010: (Start)
%F A047233 G.f.: 2*x^2*(2 + x)/((1 + x)*(1 - x)^2).
%F A047233 a(n) = a(n-1) + a(n-2) - a(n-3) for n>3.
%F A047233 a(n) = (6*n + (-1)^n - 5)/2. (End)
%F A047233 a(n) = 6*n - a(n-1) - 8 for n>1, a(1)=0. - _Vincenzo Librandi_, Aug 05 2010
%F A047233 a(n+1) = Sum_{k>=0} A030308(n,k)*A058764(k+1). - _Philippe Deléham_, Oct 17 2011
%F A047233 Sum_{n>=2} (-1)^n/a(n) = log(3)/4 - sqrt(3)*Pi/36. - _Amiram Eldar_, Dec 13 2021
%F A047233 E.g.f.: 2 + ((6*x -5)*exp(x) + exp(-x))/2. - _David Lovler_, Aug 25 2022
%t A047233 Flatten[{#,#+4}&/@(6Range[0,30])] (* _Harvey P. Dale_, Jul 07 2013 *)
%o A047233 (PARI) forstep(n=0,200,[4,2],print1(n", ")) \\ _Charles R Greathouse IV_, Oct 17 2011
%Y A047233 Cf. A047241: (6*n - (-1)^n - 5)/2.
%Y A047233 Cf. A342819.
%K A047233 nonn,easy
%O A047233 1,2
%A A047233 _N. J. A. Sloane_