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A063210 Dimension of the space of weight 2n cuspidal newforms for Gamma_0( 42 ). 2
1, 2, 6, 6, 10, 10, 14, 14, 18, 18, 22, 22, 26, 26, 30, 30, 34, 34, 38, 38, 42, 42, 46, 46, 50, 50, 54, 54, 58, 58, 62, 62, 66, 66, 70, 70, 74, 74, 78, 78, 82, 82, 86, 86, 90, 90, 94, 94, 98, 98 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Equals triangle A153860 * [1,2,3,...]. - Gary W. Adamson, Jan 03 2009

LINKS

Table of n, a(n) for n=1..50.

William A. Stein, Dimensions of the spaces S_k^{new}(Gamma_0(N))

William A. Stein, The modular forms database

Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

FORMULA

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

Except for the first term, a(n) = 4*(n-1) - a(n-1), (with a(2)=2). - Vincenzo Librandi, Dec 07 2010

From Colin Barker, Sep 08 2013: (Start)

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

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

MATHEMATICA

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 *)

PROG

(PARI) Vec(-x*(x^3-3*x^2-x-1)/((x-1)^2*(x+1)) + O(x^100)) \\ Colin Barker, Sep 08 2013

CROSSREFS

Cf. A153860. - Gary W. Adamson, Jan 03 2009

Sequence in context: A006955 A306745 A196053 * A114718 A102261 A245486

Adjacent sequences:  A063207 A063208 A063209 * A063211 A063212 A063213

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Jul 10 2001

STATUS

approved

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Last modified February 20 21:47 EST 2020. Contains 332084 sequences. (Running on oeis4.)