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%I #51 Mar 21 2024 00:45:26
%S 2,10,18,26,34,42,50,58,66,74,82,90,98,106,114,122,130,138,146,154,
%T 162,170,178,186,194,202,210,218,226,234,242,250,258,266,274,282,290,
%U 298,306,314,322,330,338,346,354,362,370,378,386,394,402,410,418,426
%N a(n) = 8*n + 2.
%C Apart from initial term(s), dimension of the space of weight 2n cusp forms for Gamma_0( 33 ).
%C Apart from initial term(s), dimension of the space of weight 2n cuspidal newforms for Gamma_0( 81 ).
%C First differences of A002939. - _Aaron David Fairbanks_, May 13 2014
%H Vincenzo Librandi, <a href="/A017089/b017089.txt">Table of n, a(n) for n = 0..5000</a>
%H Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>.
%H William A. Stein, <a href="http://wstein.org/Tables/dimskg0n.gp">Dimensions of the spaces S_k(Gamma_0(N))</a>.
%H William A. Stein, <a href="http://wstein.org/Tables/dimskg0new.gp">Dimensions of the spaces S_k^{new}(Gamma_0(N))</a>.
%H William A. Stein, <a href="http://wstein.org/Tables/">The modular forms database</a>.
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).
%F a(n) = 8*n+2; a(n) = 2*a(n-1)-a(n-2). - _Vincenzo Librandi_, May 28 2011
%F Sum_{n>=0} (-1)^n/a(n) = (Pi + 2*log(cot(Pi/8)))/(8*sqrt(2)). - _Amiram Eldar_, Dec 11 2021
%F From _Elmo R. Oliveira_, Mar 17 2024: (Start)
%F G.f.: 2*(1+3*x)/(1-x)^2.
%F E.g.f.: 2*exp(x)*(1 + 4*x).
%F a(n) = 2*A016813(n) = A008590(n) + 2. (End)
%p A017089:=n->8*n+2; seq(A017089(n), n=0..50); # _Wesley Ivan Hurt_, May 13 2014
%t Range[2, 1000, 8] (* _Vladimir Joseph Stephan Orlovsky_, May 27 2011 *)
%o (Magma) [8*n+2: n in [0..60]]; // _Vincenzo Librandi_, May 28 2011
%o (Haskell)
%o a017089 = (+ 2) . (* 8)
%o a017089_list = [2, 10 ..] -- _Reinhard Zumkeller_, Jun 07 2015
%o (PARI) a(n) = 8*n+2; \\ _Michel Marcus_, Sep 17 2015
%Y Cf. A002939, A008589, A008590, A016813, A016993, A017005, A017017, A017077.
%K nonn,easy
%O 0,1
%A _N. J. A. Sloane_, Dec 11 1996
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