A017557 a(n) = 12*n + 3.

3, 15, 27, 39, 51, 63, 75, 87, 99, 111, 123, 135, 147, 159, 171, 183, 195, 207, 219, 231, 243, 255, 267, 279, 291, 303, 315, 327, 339, 351, 363, 375, 387, 399, 411, 423, 435, 447, 459, 471, 483, 495, 507, 519, 531, 543, 555, 567, 579, 591, 603, 615, 627, 639

Offset

0,1

Comments

Apart from initial term(s), dimension of the space of weight 2n cusp forms for Gamma_0( 44 ).

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

A089911(2*a(n)) = 8. - Reinhard Zumkeller, Jul 05 2013

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

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

E.g.f.: 3*(1+4*x)*exp(x). (End)

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

Maple

seq(12*n+3, n=0..60); # G. C. Greubel, Sep 18 2019

Mathematica

12*Range[0, 60]+3 (* Vladimir Joseph Stephan Orlovsky, Feb 19 2011 *)

Prog

(Magma) [12*n+3: n in [0..60]]; // Vincenzo Librandi, Jun 07 2011
(Haskell)
a017557 = (+ 3) . (* 12)  -- Reinhard Zumkeller, Jul 05 2013
(PARI) a(n)=12*n+3 \\ Charles R Greathouse IV, Jul 10 2016
(Sage) [12*n+3 for n in (0..60)] # G. C. Greubel, Sep 18 2019
(GAP) List([0..60], n-> 12*n+3 ); # G. C. Greubel, Sep 18 2019

Crossrefs

Cf. A008594, A016813, A017533, A017545, A089911.

Sequence in context: A121250 A105549 A080065 * A147041 A347536 A002259

Adjacent sequences: A017554 A017555 A017556 * A017558 A017559 A017560

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved