This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A017593 #78 Apr 04 2025 10:20:20
%S A017593 6,18,30,42,54,66,78,90,102,114,126,138,150,162,174,186,198,210,222,
%T A017593 234,246,258,270,282,294,306,318,330,342,354,366,378,390,402,414,426,
%U A017593 438,450,462,474,486,498,510,522,534,546,558,570,582,594,606,618,630,642
%N A017593 a(n) = 12*n + 6.
%C A017593 Apart from initial term(s), dimension of the space of weight 2n cuspidal newforms for Gamma_0(73).
%C A017593 Continued fraction expansion of tanh(1/6). - _Benoit Cloitre_, Dec 17 2002
%C A017593 Also solutions to 5^x + 7^x == 11 (mod 13). - _Cino Hilliard_, May 10 2003
%C A017593 Numbers m such that the sum of the m-th powers of all 2 X 2 matrices over Z/mZ is a nonzero matrix. - _José María Grau Ribas_, Jan 31 2014
%C A017593 Positive numbers k for which 1/2 + k/4 + k^2/6 is an integer. - _Bruno Berselli_, Apr 12 2018
%H A017593 P. Fortuny, J. M. Grau, A. M. Oller-Marcén and I. F. Rúa, <a href="http://arxiv.org/abs/1505.08132">On power sums of matrices over a finite commutative ring</a>, arXiv:1505.08132 [math.RA], 2015.
%H A017593 Milan Janjic and Boris Petkovic, <a href="http://arxiv.org/abs/1301.4550">A Counting Function</a>, arXiv 1301.4550 [math.CO], 2013.
%H A017593 Luis Manuel Rivera, <a href="http://arxiv.org/abs/1406.3081">Integer sequences and k-commuting permutations</a>, arXiv preprint arXiv:1406.3081 [math.CO], 2014-2015.
%H A017593 William A. Stein, <a href="http://wstein.org/Tables/dimskg0new.gp">Dimensions of the spaces S_k^{new}(Gamma_0(N))</a>.
%H A017593 William A. Stein, <a href="http://wstein.org/Tables/">The modular forms database</a>.
%H A017593 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).
%F A017593 A030133(a(n)) = 9. - _Reinhard Zumkeller_, Jul 04 2007
%F A017593 a(n) = 24*n - a(n-1) with n > 0, a(0)=6. - _Vincenzo Librandi_, Nov 19 2010
%F A017593 a(0)=6, a(1)=18; for n > 1, a(n) = 2*a(n-1) - a(n-2). - _Harvey P. Dale_, Aug 20 2014
%F A017593 G.f.: 6*(1+x)/(1-x)^2. - _Wolfdieter Lang_, Oct 27 2020
%F A017593 Sum_{n>=0} (-1)^n/a(n) = Pi/24 (A019691). - _Amiram Eldar_, Dec 12 2021
%F A017593 From _Amiram Eldar_, Nov 24 2024: (Start)
%F A017593 Product_{n>=0} (1 - (-1)^n/a(n)) = sqrt(2) * sin(5*Pi/24).
%F A017593 Product_{n>=0} (1 + (-1)^n/a(n)) = sqrt(2) * cos(5*Pi/24). (End)
%F A017593 From _Elmo R. Oliveira_, Apr 04 2025: (Start)
%F A017593 E.g.f.: 6*exp(x)*(1 + 2*x).
%F A017593 a(n) = 6*A005408(n) = 3*A016825(n) = 2*A016945(n). (End)
%t A017593 12 Range[0, 200] + 6 (* _Vladimir Joseph Stephan Orlovsky_, Feb 19 2011 *)
%t A017593 LinearRecurrence[{2, -1}, {6, 18}, 60] (* _Harvey P. Dale_, Aug 20 2014 *)
%o A017593 (Sage) [i+6 for i in range(645) if gcd(i,12) == 12] # _Zerinvary Lajos_, May 21 2009
%o A017593 (PARI) a(n)=12*n+6 \\ _Charles R Greathouse IV_, Sep 24 2015
%Y A017593 Cf. A005408, A016825, A016945, A017641, A019691, A030133.
%K A017593 nonn,easy
%O A017593 0,1
%A A017593 _N. J. A. Sloane_
%E A017593 Typos in sequence (270 was 2,70 and 510 was 5,10) fixed by _Peter Luschny_, Dec 14 2009