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A047510 Numbers that are congruent to {2, 4, 6, 7} mod 8.

%I A047510 #16 Sep 08 2022 08:44:57
%S A047510 2,4,6,7,10,12,14,15,18,20,22,23,26,28,30,31,34,36,38,39,42,44,46,47,
%T A047510 50,52,54,55,58,60,62,63,66,68,70,71,74,76,78,79,82,84,86,87,90,92,94,
%U A047510 95,98,100,102,103,106,108,110,111,114,116,118,119,122,124
%N A047510 Numbers that are congruent to {2, 4, 6, 7} mod 8.
%H A047510 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,1,-1).
%F A047510 From _Wesley Ivan Hurt_, May 27 2016: (Start)
%F A047510 G.f.: x*(2+2*x+2*x^2+x^3+x^4) / ((x-1)^2*(1+x+x^2+x^3)).
%F A047510 a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.
%F A047510 a(n) = (8*n-1-i^(2*n)-i^(-n)-i^n)/4 where i=sqrt(-1).
%F A047510 a(2k) = A047535(k), a(2k-1) = A016825(k-1) for k>0. (End)
%F A047510 E.g.f.: (2 - cos(x) + 4*x*sinh(x) + (4*x - 1)*cosh(x))/2. - _Ilya Gutkovskiy_, May 27 2016
%F A047510 Sum_{n>=1} (-1)^(n+1)/a(n) = (sqrt(2)+1)*Pi/16 - sqrt(2)*log(2*sqrt(2)+3)/16. - _Amiram Eldar_, Dec 25 2021
%p A047510 A047510:=n->(8*n-1-I^(2*n)-I^(-n)-I^n)/4: seq(A047510(n), n=1..100); # _Wesley Ivan Hurt_, May 27 2016
%t A047510 Table[(8n-1-I^(2n)-I^(-n)-I^n)/4, {n, 80}] (* _Wesley Ivan Hurt_, May 27 2016 *)
%o A047510 (Magma) [n : n in [0..150] | n mod 8 in [2, 4, 6, 7]]; // _Wesley Ivan Hurt_, May 27 2016
%Y A047510 Cf. A016825, A047535.
%K A047510 nonn,easy
%O A047510 1,1
%A A047510 _N. J. A. Sloane_