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A047410 Numbers that are congruent to {2, 4, 6} mod 8. 1

%I

%S 2,4,6,10,12,14,18,20,22,26,28,30,34,36,38,42,44,46,50,52,54,58,60,62,

%T 66,68,70,74,76,78,82,84,86,90,92,94,98,100,102,106,108,110,114,116,

%U 118,122,124,126,130,132,134,138,140,142,146,148,150,154,156,158

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

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

%H William A. Stein, <a href="http://modular.math.washington.edu/Tables/dimskg0new.gp">Dimensions of the spaces S_k^{new}(Gamma_0(N))</a>

%H William A. Stein, <a href="http://wstein.org/Tables/">The modular forms database</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,1,-1).

%F a(n) = 2*floor((n-1)/3) + 2*n. - _Gary Detlefs_, Mar 18 2010

%F From _R. J. Mathar_, Dec 05 2011 (Start)

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

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

%F 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

%F From _Wesley Ivan Hurt_, Jun 09 2016: (Start)

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

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

%p 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

%t 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 *)

%o (MAGMA) [n : n in [0..150] | n mod 8 in [2, 4, 6]]; // _Wesley Ivan Hurt_, Jun 09 2016

%Y Cf. A042968.

%K nonn,easy

%O 1,1

%A _N. J. A. Sloane_

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Last modified August 22 02:44 EDT 2019. Contains 326169 sequences. (Running on oeis4.)