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%I #40 May 22 2023 11:38:03
%S 0,1,4,6,8,9,12,14,16,17,20,22,24,25,28,30,32,33,36,38,40,41,44,46,48,
%T 49,52,54,56,57,60,62,64,65,68,70,72,73,76,78,80,81,84,86,88,89,92,94,
%U 96,97,100,102,104,105,108,110,112,113,116,118,120,121,124
%N Numbers that are congruent to {0, 1, 4, 6} mod 8.
%C All squares and the products of any terms belong to the sequence. This sequence (n > 1) is closed under multiplication. - _Klaus Purath_, Feb 13 2023
%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*(1 + 3*x + 2*x^2 + 2*x^3) / ( (1+x)*(x^2+1)*(x-1)^2 ). - _R. J. Mathar_, Dec 05 2011
%F From _Wesley Ivan Hurt_, May 24 2016: (Start)
%F a(n) = a(n-1) + a(n-4) - a(n-5) for n > 5.
%F a(n) = (8*n - 9 - i^(2n) + i^(-n) + i^n)/4 where i=sqrt(-1).
%F a(2k) = A047452(k), a(2k-1) = A008586(k-1) for k > 0. (End)
%F E.g.f.: (4 + cos(x) + 4*(x - 1)*sinh(x) + (4*x - 5)*cosh(x))/2. - _Ilya Gutkovskiy_, May 25 2016
%F Sum_{n>=2} (-1)^n/a(n) = sqrt(2)*Pi/16 + (10 - sqrt(2))*log(2)/16 + sqrt(2)*log(2 + sqrt(2))/8. - _Amiram Eldar_, Dec 20 2021
%p A047409:=n->(8*n-9-I^(2*n)+I^(-n)+I^n)/4: seq(A047409(n), n=1..100); # _Wesley Ivan Hurt_, May 24 2016
%t Select[Range[0,110], MemberQ[{0,1,4,6}, Mod[#,8]]&] (* _Harvey P. Dale_, Sep 28 2011 *)
%o (Magma) [n : n in [0..150] | n mod 8 in [0, 1, 4, 6]]; // _Wesley Ivan Hurt_, May 24 2016
%Y Cf. A008586, A047452.
%K nonn,easy
%O 1,3
%A _N. J. A. Sloane_
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