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A047410 Numbers that are congruent to {2, 4, 6} mod 8. 1
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 (list; graph; refs; listen; history; text; internal format)
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)

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.

Sequence in context: A175817 A256773 A141104 * A255056 A164875 A301646

Adjacent sequences:  A047407 A047408 A047409 * A047411 A047412 A047413

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified July 21 19:13 EDT 2019. Contains 325199 sequences. (Running on oeis4.)