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A017581 a(n) = 12*n + 5.

%I A017581 #43 Apr 11 2025 01:26:48
%S A017581 5,17,29,41,53,65,77,89,101,113,125,137,149,161,173,185,197,209,221,
%T A017581 233,245,257,269,281,293,305,317,329,341,353,365,377,389,401,413,425,
%U A017581 437,449,461,473,485,497,509,521,533,545,557,569,581,593,605,617,629
%N A017581 a(n) = 12*n + 5.
%C A017581 Apart from initial term(s), dimension of the space of weight 2n cusp forms for Gamma_0(71).
%C A017581 A089911(2*a(n)) = 7. - _Reinhard Zumkeller_, Jul 05 2013
%C A017581 Equivalently, intersection of A016813 and A016789. - _Bruno Berselli_, Jan 24 2018
%H A017581 Vincenzo Librandi, <a href="/A017581/b017581.txt">Table of n, a(n) for n = 0..3000</a>
%H A017581 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>.
%H A017581 William A. Stein, <a href="http://wstein.org/Tables/dimskg0n.gp">Dimensions of the spaces S_k(Gamma_0(N))</a>.
%H A017581 William A. Stein, <a href="http://wstein.org/Tables/">The modular forms database</a>.
%H A017581 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).
%F A017581 a(n) = 2*a(n-1) - a(n-2) for n>1, a(0)=5, a(1)=17. - _Vincenzo Librandi_, Jun 08 2011
%F A017581 G.f.: x*(5 + 7*x)/(1 - x)^2. - _Wolfdieter Lang_, Jul 04 2023
%F A017581 E.g.f.: exp(x)*(5 + 12*x). - _Stefano Spezia_, Feb 21 2024
%F A017581 a(n) = A016969(2*n) = A016789(4*n+1). - _Elmo R. Oliveira_, Apr 10 2025
%t A017581 12*Range[0,200]+5 (* _Vladimir Joseph Stephan Orlovsky_, Feb 19 2011 *)
%o A017581 (Magma) [12*n+5: n in [0..60]]; // _Vincenzo Librandi_, Jun 08 2011
%o A017581 (Haskell)
%o A017581 a017581 = (+ 5) . (* 12)  -- _Reinhard Zumkeller_, Jul 05 2013
%o A017581 (PARI) a(n)=12*n+5 \\ _Charles R Greathouse IV_, Jul 10 2016
%Y A017581 Cf. A008594, A016789, A016813, A016969, A017533, A017545, A017593, A089911.
%K A017581 nonn,easy
%O A017581 0,1
%A A017581 _N. J. A. Sloane_