A017089 a(n) = 8*n + 2.

2, 10, 18, 26, 34, 42, 50, 58, 66, 74, 82, 90, 98, 106, 114, 122, 130, 138, 146, 154, 162, 170, 178, 186, 194, 202, 210, 218, 226, 234, 242, 250, 258, 266, 274, 282, 290, 298, 306, 314, 322, 330, 338, 346, 354, 362, 370, 378, 386, 394, 402, 410, 418, 426

Offset: 0

Author

N. J. A. Sloane, Dec 11 1996

Keywords

• nonn
• easy

Comments

Apart from initial term(s), dimension of the space of weight 2n cusp forms for Gamma_0( 33 ).

Apart from initial term(s), dimension of the space of weight 2n cuspidal newforms for Gamma_0( 81 ).

First differences of A002939. - Aaron David Fairbanks, May 13 2014

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..5000
• Tanya Khovanova, Recursive Sequences.
• William A. Stein, Dimensions of the spaces S_k(Gamma_0(N)).
• 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 (2,-1).

Crossrefs

Cf. A002939, A008589, A008590, A016813, A016993, A017005, A017017, A017077.

Programs

Haskell

a017089 = (+ 2) . (* 8)
a017089_list = [2, 10 ..]  -- Reinhard Zumkeller, Jun 07 2015

Magma

[8*n+2: n in [0..60]]; // Vincenzo Librandi, May 28 2011

Maple

A017089:=n->8*n+2; seq(A017089(n), n=0..50); # Wesley Ivan Hurt, May 13 2014

Mathematica

Range[2, 1000, 8] (* Vladimir Joseph Stephan Orlovsky, May 27 2011 *)

PARI

a(n) = 8*n+2; \\ Michel Marcus, Sep 17 2015

Formula

a(n) = 8*n+2; a(n) = 2*a(n-1)-a(n-2). - Vincenzo Librandi, May 28 2011

Sum_{n>=0} (-1)^n/a(n) = (Pi + 2*log(cot(Pi/8)))/(8*sqrt(2)). - Amiram Eldar, Dec 11 2021

From Elmo R. Oliveira, Mar 17 2024: (Start)

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

E.g.f.: 2*exp(x)*(1 + 4*x).

a(n) = 2*A016813(n) = A008590(n) + 2. (End)