A017545 a(n) = 12*n + 2.

2, 14, 26, 38, 50, 62, 74, 86, 98, 110, 122, 134, 146, 158, 170, 182, 194, 206, 218, 230, 242, 254, 266, 278, 290, 302, 314, 326, 338, 350, 362, 374, 386, 398, 410, 422, 434, 446, 458, 470, 482, 494, 506, 518, 530, 542, 554, 566, 578, 590, 602, 614, 626, 638

Offset

0,1

Comments

Apart from initial term(s), dimension of the space of weight 2n cusp forms for Gamma_0( 40 ).

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..2000

Tanya Khovanova, Recursive Sequences.

William A. Stein, Dimensions of the spaces S_k(Gamma_0(N)).

William A. Stein, The modular forms database.

Index entries for linear recurrences with constant coefficients, signature (2,-1).

Formula

a(n) = 2*a(n-1) - a(n-2). - Vincenzo Librandi, Jun 07 2011

From G. C. Greubel, Sep 18 2019: (Start)

G.f.: 2*(1 + 5*x)/(1-x)^2.

E.g.f.: 2*(1 + 6*x)*exp(x). (End)

Sum_{n>=0} (-1)^n/a(n) = Pi/12 + sqrt(3)*log(2 + sqrt(3))/12. - Amiram Eldar, Dec 12 2021

Maple

A017545:=n->12*n+2: seq(A017545(n), n=0..60); # Wesley Ivan Hurt, Apr 27 2017

Mathematica

12*Range[0, 60]+2 (* Vladimir Joseph Stephan Orlovsky, Feb 19 2011 *)

Prog

(Magma) [12*n+2: n in [0..60]]; // Vincenzo Librandi, Jun 07 2011
(PARI) a(n)=12*n+2 \\ Charles R Greathouse IV, Jul 10 2016
(Sage) [2*(6*n+1) for n in (0..60)] # G. C. Greubel, Sep 18 2019
(GAP) List([0..60], n-> 2*(6*n+1) ); # G. C. Greubel, Sep 18 2019

Crossrefs

Cf. A008594, A017533, A017557.

Subsequence of A072065.

Sequence in context: A174594 A051222 A194411 * A280268 A109080 A295083

Adjacent sequences: A017542 A017543 A017544 * A017546 A017547 A017548

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved