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%I #20 Feb 14 2024 02:25:44
%S 19,1801,249697,35842177,5159904769,743009863681,106993223294977,
%T 15407021789577217,2218611109320327169,319479999401581608961,
%U 46005119909741205651457,6624737266953695061344257,953962166440743626203987969
%N a(n) = 12^(2n+1) + 6 * 12^n + 1: the right Aurifeuillian factor of 12^(6n+3) + 1.
%C The corresponding left Aurifeuillian factor is A220989.
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Cunningham_project">Cunningham Project</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (157,-1884,1728).
%F Aurifeuillian factorization: 12^(6n+3) + 1 = (12^(2n+1) + 1) * A220989(n) * a(n).
%F G.f.: -(2736*x^2-1182*x+19) / ((x-1)*(12*x-1)*(144*x-1)). - _Colin Barker_, Jan 03 2013
%t Table[12^(2n+1) + 6 * 12^n + 1, {n, 0, 10}]
%t LinearRecurrence[{157,-1884,1728},{19,1801,249697},20] (* _Harvey P. Dale_, Mar 26 2022 *)
%o (PARI) a(n)=12^(2*n+1)+6*12^n+1 \\ _Charles R Greathouse IV_, Sep 28 2015
%Y Cf. A092440, A085601, A220978, A198410, A220979-A220989.
%K nonn,easy
%O 0,1
%A _Stuart Clary_, Dec 27 2012
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