A047410 Numbers that are congruent to {2, 4, 6} mod 8.

2, 4, 6, 10, 12, 14, 18, 20, 22, 26, 28, 30, 34, 36, 38, 42, 44, 46, 50, 52, 54, 58, 60, 62, 66, 68, 70, 74, 76, 78, 82, 84, 86, 90, 92, 94, 98, 100, 102, 106, 108, 110, 114, 116, 118, 122, 124, 126, 130, 132, 134, 138, 140, 142, 146, 148, 150, 154, 156, 158

Offset

1,1

Comments

Apart from initial term(s), dimension of the space of weight 2n cuspidal newforms for Gamma_0( 17 ).

Links

Table of n, a(n) for n=1..60.

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 (1,0,1,-1).

Formula

a(n) = 2*floor((n-1)/3) + 2*n. - Gary Detlefs, Mar 18 2010

From R. J. Mathar, Dec 05 2011: (Start)

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

a(n) = 2*A042968(n). (End)

a(n) = a(n-1) + a(n-3) - a(n-4) for n>4, with a(1)=2, a(2)=4, a(3)=6, a(4)=10. - Harvey P. Dale, Oct 06 2014

From Wesley Ivan Hurt, Jun 09 2016: (Start)

a(n) = 2*(12*n-6-3*cos(2*n*Pi/3)+sqrt(3)*sin(2*n*Pi/3))/9.

a(3k) = 8k-2, a(3k-1) = 8k-4, a(3k-2) = 8k-6. (End)

Sum_{n>=1} (-1)^(n+1)/a(n) = (2*sqrt(2)-1)*Pi/16. - Amiram Eldar, Dec 19 2021

E.g.f.: 2*(9 + 6*exp(x)*(2*x - 1) - exp(-x/2)*(3*cos(sqrt(3)*x/2) - sqrt(3)*sin(sqrt(3)*x/2)))/9. - Stefano Spezia, Oct 17 2022

Maple

A047410:=n->2*(12*n-6-3*cos(2*n*Pi/3)+sqrt(3)*sin(2*n*Pi/3))/9: seq(A047410(n), n=1..100); # Wesley Ivan Hurt, Jun 09 2016

Mathematica

With[{upto=140}, Complement[2*Range[upto/2], 8*Range[upto/8]]] (* or *) LinearRecurrence[{1, 0, 1, -1}, {2, 4, 6, 10}, 60] (* Harvey P. Dale, Oct 06 2014 *)

Prog

(Magma) [n : n in [0..150] | n mod 8 in [2, 4, 6]]; // Wesley Ivan Hurt, Jun 09 2016

Crossrefs

Cf. A042968, A047395, A047407, A047464.

Sequence in context: A175817 A256773 A141104 * A339331 A255056 A164875

Adjacent sequences: A047407 A047408 A047409 * A047411 A047412 A047413

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved