login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

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

%I #19 Aug 01 2015 10:40:44

%S 1,19,217,2107,19441,176419,1592137,14342347,129120481,1162202419,

%T 10460176057,94142647387,847287015121,7625592702019,68630363015977,

%U 617673353237227,5559060437415361,50031544711579219,450283904728735897,4052555149532191867

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

%C The corresponding right Aurifeuillian factor is A198410(n+2): 3^(6*n+3) + 1 = (3^(2*n+1) + 1) * a(n) * A198410(n+2).

%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 (13, -39, 27).

%F a(n) = 13*a(n-1) - 39*a(n-2) + 27*a(n-3).

%F G.f.: (1 + 3*x)^2/((1 - x)*(1 - 3*x)*(1 - 9*x)).

%t Table[3^(2n+1) - 3^(n+1) + 1, {n, 0, 30}]

%t LinearRecurrence[{13,-39,27},{1,19,217},30] (* _Harvey P. Dale_, Mar 17 2013 *)

%o (PARI) Vec((1 + 3*x)^2/((1 - x)*(1 - 3*x)*(1 - 9*x)) + O(x^30)) \\ _Michel Marcus_, Feb 12 2015

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

%K nonn,easy

%O 0,2

%A _Stuart Clary_, Dec 27 2012