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Dimension of the space of weight 2n cuspidal newforms for Gamma_0( 42 ).
2

%I #29 Aug 22 2019 12:18:12

%S 1,2,6,6,10,10,14,14,18,18,22,22,26,26,30,30,34,34,38,38,42,42,46,46,

%T 50,50,54,54,58,58,62,62,66,66,70,70,74,74,78,78,82,82,86,86,90,90,94,

%U 94,98,98

%N Dimension of the space of weight 2n cuspidal newforms for Gamma_0( 42 ).

%C Equals triangle A153860 * [1,2,3,...]. - _Gary W. Adamson_, Jan 03 2009

%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 a(n) = (n^2 - n)/floor(n/2) for n >=2. (Excludes leading 1.) - _William A. Tedeschi_, Mar 20 2008

%F Except for the first term, a(n) = 4*(n-1) - a(n-1), (with a(2)=2). - _Vincenzo Librandi_, Dec 07 2010

%F From _Colin Barker_, Sep 08 2013: (Start)

%F a(n) = a(n-1) + a(n-2) - a(n-3) for n > 4.

%F G.f.: -x*(x^3-3*x^2-x-1) / ((x-1)^2*(x+1)). (End)

%t With[{c=Range[6,102,4]},Join[{1,2},Riffle[c,c]]] (* or *) LinearRecurrence[ {1,1,-1},{1,2,6,6,10},50] (* _Harvey P. Dale_, Jun 22 2019 *)

%o (PARI) Vec(-x*(x^3-3*x^2-x-1)/((x-1)^2*(x+1)) + O(x^100)) \\ _Colin Barker_, Sep 08 2013

%Y Cf. A153860. - _Gary W. Adamson_, Jan 03 2009

%K nonn,easy

%O 1,2

%A _N. J. A. Sloane_, Jul 10 2001