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%I #25 Dec 25 2023 13:27:59
%S 0,2,5,6,8,10,13,14,16,18,21,22,24,26,29,30,32,34,37,38,40,42,45,46,
%T 48,50,53,54,56,58,61,62,64,66,69,70,72,74,77,78,80,82,85,86,88,90,93,
%U 94,96,98,101,102,104,106,109,110,112,114,117,118,120,122,125
%N Numbers that are congruent to {0, 2, 5, 6} 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 G.f.: x^2*(2+3*x+x^2+2*x^3) / ( (1+x)*(x^2+1)*(x-1)^2 ). - _R. J. Mathar_, Dec 07 2011
%F From _Wesley Ivan Hurt_, May 26 2016: (Start)
%F a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.
%F a(n) = (8*n-7-i^(2*n)-i^(1-n)+i^(1+n))/4 where i=sqrt(-1).
%F a(2k) = A130824(k) k>0, a(2k-1) = A047615(k). (End)
%F E.g.f.: (4 - sin(x) + (4*x - 3)*sinh(x) + 4*(x - 1)*cosh(x))/2. - _Ilya Gutkovskiy_, May 27 2016
%F a(n) = (8*n-7-cos(n*Pi)-2*sin(n*Pi/2))/4. - _Wesley Ivan Hurt_, Oct 05 2017
%F Sum_{n>=2} (-1)^n/a(n) = (sqrt(2)-1)*Pi/16 + (4-sqrt(2))*log(2)/16 + sqrt(2)*log(2+sqrt(2))/8. - _Amiram Eldar_, Dec 21 2021
%p A047441:=n->(8*n-7-I^(2*n)-I^(1-n)+I^(1+n))/4: seq(A047441(n), n=1..100); # _Wesley Ivan Hurt_, May 26 2016
%t Table[(8n-7-I^(2n)-I^(1-n)+I^(1+n))/4, {n, 80}] (* _Wesley Ivan Hurt_, May 26 2016 *)
%t LinearRecurrence[{1,0,0,1,-1},{0,2,5,6,8},100] (* _Harvey P. Dale_, Dec 25 2023 *)
%o (Magma) [n : n in [0..150] | n mod 8 in [0, 2, 5, 6]]; // _Wesley Ivan Hurt_, May 26 2016
%Y Cf. A047615, A130824.
%K nonn,easy
%O 1,2
%A _N. J. A. Sloane_
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