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%I #21 Apr 29 2023 14:14:34
%S 0,2,4,7,8,10,12,15,16,18,20,23,24,26,28,31,32,34,36,39,40,42,44,47,
%T 48,50,52,55,56,58,60,63,64,66,68,71,72,74,76,79,80,82,84,87,88,90,92,
%U 95,96,98,100,103,104,106,108,111,112,114,116,119,120,122,124
%N Numbers that are congruent to {0, 2, 4, 7} mod 8.
%C The products of an odd number of terms as well as products of one term each of this sequence and one term of A047409 are members. The products of an even number of terms belong to A047409. The union of this sequence and A047409 is closed under multiplication. - _Klaus Purath_, Apr 23 2023
%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 29 2016: (Start)
%F G.f.: x^2*(2+2*x+3*x^2+x^3) / ((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-7+i^(2*n)+i^(-n)+i^n)/4 where i=sqrt(-1).
%F a(2k) = A047524(k), a(2k-1) = A008586(k-1) for k>0. (End)
%F Sum_{n>=2} (-1)^n/a(n) = (10-sqrt(2))*log(2)/16 + sqrt(2)*log(2+sqrt(2))/8 - sqrt(2)*Pi/16. - _Amiram Eldar_, Dec 21 2021
%p A047540:=n->(8*n-7+I^(2*n)+I^(-n)+I^n)/4: seq(A047540(n), n=1..100); # _Wesley Ivan Hurt_, May 29 2016
%t Table[(8n-7+I^(2n)+I^(-n)+I^n)/4, {n, 80}] (* _Wesley Ivan Hurt_, May 29 2016 *)
%t {0,2,4,7}+#&/@(8*Range[0,20])//Flatten (* _Harvey P. Dale_, Dec 20 2022 *)
%o (Magma) [n : n in [0..150] | n mod 8 in [0, 2, 4, 7]]; // _Wesley Ivan Hurt_, May 29 2016
%Y Cf. A008586, A047524.
%K nonn,easy
%O 1,2
%A _N. J. A. Sloane_
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