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A047430 Numbers that are congruent to {0, 4, 5, 6} mod 8.

%I A047430 #29 Aug 05 2023 10:46:54
%S A047430 0,4,5,6,8,12,13,14,16,20,21,22,24,28,29,30,32,36,37,38,40,44,45,46,
%T A047430 48,52,53,54,56,60,61,62,64,68,69,70,72,76,77,78,80,84,85,86,88,92,93,
%U A047430 94,96,100,101,102,104,108,109,110,112,116,117,118,120,124
%N A047430 Numbers that are congruent to {0, 4, 5, 6} mod 8.
%H A047430 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,1,-1).
%F A047430 G.f.: x^2*(4+x+x^2+2*x^3) / ( (1+x)*(x^2+1)*(x-1)^2 ). - _R. J. Mathar_, Dec 07 2011
%F A047430 From _Wesley Ivan Hurt_, May 25 2016: (Start)
%F A047430 a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.
%F A047430 a(n) = (8*n-5+i^(2*n)-(2+i)*i^(-n)-(2-i)*i^n)/4 where i=sqrt(-1).
%F A047430 a(2k) = A047406(k), a(2k-1) = A047615(k). (End)
%F A047430 E.g.f.: (4 - sin(x) - 2*cos(x) + (4*x - 3)*sinh(x) + (4*x - 2)*cosh(x))/2. - _Ilya Gutkovskiy_, May 25 2016
%F A047430 Sum_{n>=2} (-1)^n/a(n) = sqrt(2)*log(2+sqrt(2))/8 - (2-sqrt(2))*(Pi-log(2))/16. - _Amiram Eldar_, Dec 23 2021
%p A047430 A047430:=n->(8*n-5+I^(2*n)-(2+I)*I^(-n)-(2-I)*I^n)/4: seq(A047430(n), n=1..100); # _Wesley Ivan Hurt_, May 25 2016
%t A047430 Table[(8n-5+I^(2n)-(2+I)*I^(-n)-(2-I)*I^n)/4, {n, 80}] (* _Wesley Ivan Hurt_, May 25 2016 *)
%t A047430 Select[Range[0, 124], MemberQ[{0, 4, 5, 6}, Mod[#, 8]] &] (* _Michael De Vlieger_, May 25 2016 *)
%t A047430 LinearRecurrence[{1,0,0,1,-1},{0,4,5,6,8},100] (* _Harvey P. Dale_, Aug 05 2023 *)
%o A047430 (Magma) [n : n in [0..150] | n mod 8 in [0, 4, 5, 6]]; // _Wesley Ivan Hurt_, May 25 2016
%Y A047430 Cf. A047406, A047615.
%K A047430 nonn,easy
%O A047430 1,2
%A A047430 _N. J. A. Sloane_