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%I #37 Sep 05 2022 09:10:57
%S 1,4,13,16,25,28,37,40,49,52,61,64,73,76,85,88,97,100,109,112,121,124,
%T 133,136,145,148,157,160,169,172,181,184,193,196,205,208,217,220,229,
%U 232,241,244,253,256,265,268,277,280,289,292,301,304,313,316,325
%N Numbers that are congruent to {1, 4} mod 12.
%C The squares of the terms of A001651 are the squares of this sequence. - _Bruno Berselli_, Aug 12 2013
%H Colin Barker, <a href="/A228137/b228137.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).
%F a(n) = -13/2 - 3*(-1)^n/2 + 6*n.
%F a(n) = a(n-1) + a(n-2) - a(n-3).
%F G.f.: x*(8*x^2+3*x+1) / ((x-1)^2*(x+1)).
%F Sum_{n>=1} (-1)^(n+1)/a(n) = (sqrt(3)+3)*Pi/36 + log(2)/4 - sqrt(3)*log(26-15*sqrt(3))/36. - _Amiram Eldar_, Dec 28 2021
%F E.g.f.: 8 + ((12*x - 13)*exp(x) - 3*exp(-x))/2. - _David Lovler_, Sep 04 2022
%t Select[Range[300], MemberQ[{1, 4}, Mod[#, 12]] &] (* _Amiram Eldar_, Dec 28 2021 *)
%o (PARI) Vec(x*(8*x^2+3*x+1)/((x-1)^2*(x+1)) + O(x^99))
%Y Cf. A001651, A087445, A146512, A228138.
%K nonn,easy
%O 1,2
%A _Colin Barker_, Aug 12 2013
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