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Numbers that are congruent to {2, 4, 6, 7} mod 8.
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%I #16 Sep 08 2022 08:44:57

%S 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 50,52,54,55,58,60,62,63,66,68,70,71,74,76,78,79,82,84,86,87,90,92,94,

%U 95,98,100,102,103,106,108,110,111,114,116,118,119,122,124

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

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,1,-1).

%F From _Wesley Ivan Hurt_, May 27 2016: (Start)

%F G.f.: x*(2+2*x+2*x^2+x^3+x^4) / ((x-1)^2*(1+x+x^2+x^3)).

%F a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.

%F a(n) = (8*n-1-i^(2*n)-i^(-n)-i^n)/4 where i=sqrt(-1).

%F a(2k) = A047535(k), a(2k-1) = A016825(k-1) for k>0. (End)

%F E.g.f.: (2 - cos(x) + 4*x*sinh(x) + (4*x - 1)*cosh(x))/2. - _Ilya Gutkovskiy_, May 27 2016

%F 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:=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 Table[(8n-1-I^(2n)-I^(-n)-I^n)/4, {n, 80}] (* _Wesley Ivan Hurt_, May 27 2016 *)

%o (Magma) [n : n in [0..150] | n mod 8 in [2, 4, 6, 7]]; // _Wesley Ivan Hurt_, May 27 2016

%Y Cf. A016825, A047535.

%K nonn,easy

%O 1,1

%A _N. J. A. Sloane_