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%I #16 Feb 14 2024 02:24:23
%S 911,46489241,4845303761663,560176314330212777,
%T 65739735996793498937711,7731453717973685046293120441,
%U 909551411151743369070229385367263,107007034358477098527617255914118283977,12589257482346423369016062830670344414194511
%N The right Aurifeuillian factor of 7^(14n+7) + 1.
%C The corresponding left Aurifeuillian factor is A220983.
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Cunningham_project">Cunningham Project</a>
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (137257, -2354918349, 5670354183893, -1944931485075299, 95029449572634843, -651636050170246351, 558545864083284007).
%F a(n) = 7^(6n+3) + 7^(5n+3) + 3 * 7^(4n+2) + 7^(3n+2) + 3 * 7^(2n+1) + 7^(n+1) + 1.
%F Aurifeuillian factorization: 7^(14n+7) + 1 = (7^(2n+1) + 1) * A220983(n) * a(n).
%F G.f.: -(1483484787696419039*x^6 -1087259214306211086*x^5 +71725962948861585*x^4 -562870083909028*x^3 +609660625665*x^2 -78551886*x +911) / ((x -1)*(7*x -1)*(49*x -1)*(343*x -1)*(2401*x -1)*(16807*x -1)*(117649*x -1)). [_Colin Barker_, Jan 04 2013]
%t Table[7^(6n+3) + 7^(5n+3) + 3 * 7^(4n+2) + 7^(3n+2) + 3 * 7^(2n+1) + 7^(n+1) + 1, {n, 0, 20}]
%Y Cf. A092440, A085601, A220978, A198410, A220979-A220990.
%K nonn,easy
%O 0,1
%A _Stuart Clary_, Dec 27 2012
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