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%I #44 Jan 12 2024 01:24:34
%S 5,16,24,36,44,56,64,76,84,96,104,116,124,136,144,156,164,176,184,196,
%T 204,216,224,236,244,256,264,276,284,296,304,316,324,336,344,356,364,
%U 376,384,396,404,416,424,436,444,456,464,476,484,496,504,516,524,536
%N Dimension of the space of weight 2n cuspidal newforms for Gamma_0( 77 ).
%C Also dimension of the space of weight 2n cuspidal newforms for Gamma_0( 93 ).
%H Reinhard Zumkeller, <a href="/A063232/b063232.txt">Table of n, a(n) for n = 1..1000</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_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).
%F Except for the first term, a(n) = 20*(n-1)-a(n-1), (with a(2)=16). - _Vincenzo Librandi_, Dec 07 2010
%F a(n) = -5+(-1)^n+10*n for n>1. a(n)=a(n-1)+a(n-2)-a(n-3) for n>4; G.f.: x*(x^3+3*x^2+11*x+5) / ((x-1)^2*(x+1)). - _Colin Barker_, Sep 08 2013
%F Sum_{n>=1} (-1)^(n+1)/a(n) = (sqrt(1+2/sqrt(5))*Pi - 1)/20. - _Amiram Eldar_, Jan 12 2024
%t Table[5 + 10 (n - 1) + (-1)^n + Mod[Binomial[2 (n - 1), n - 1], 2], {n, 50}] (* _Wesley Ivan Hurt_, May 25 2014 *)
%t LinearRecurrence[{1,1,-1},{5,16,24,36},60] (* _Harvey P. Dale_, Aug 21 2017 *)
%o (PARI) A063232(n)=10*n-3-bittest(n,0)*2-(n>1) \\ _M. F. Hasler_, Mar 05 2012
%o (Haskell)
%o a063232 n = a063232_list !! (n-1)
%o a063232_list = 5 : 16 : 24 : 36 : zipWith3 (((-) .) . (+))
%o (drop 3 a063232_list) (drop 2 a063232_list) (tail a063232_list)
%o -- _Reinhard Zumkeller_, May 03 2015
%K nonn,easy
%O 1,1
%A _N. J. A. Sloane_, Jul 10 2001
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