A220989 - OEIS

%I #16 Feb 14 2024 02:25:21

%S 7,1657,247969,35821441,5159655937,743006877697,106993187463169,

%T 15407021359595521,2218611104160546817,319479999339664244737,

%U 46005119908998197280769,6624737266944778960896001,953962166440636632998608897

%N a(n) = 12^(2n+1) - 6 * 12^n + 1: the left Aurifeuillian factor of 12^(6n+3) + 1.

%C The corresponding right Aurifeuillian factor is A220990.

%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) * a(n) * A220990(n).

%F G.f.: -(1008*x^2+558*x+7) / ((x-1)*(12*x-1)*(144*x-1)). [_Colin Barker_, Jan 03 2013]

%t Table[12^(2n+1) - 6 * 12^n + 1, {n, 0, 20}]

%Y Cf. A092440, A085601, A220978, A198410, A220979-A220990.

%K nonn,easy

%O 0,1

%A _Stuart Clary_, Dec 27 2012