A220990 a(n) = 12^(2n+1) + 6 * 12^n + 1: the right Aurifeuillian factor of 12^(6n+3) + 1.

19, 1801, 249697, 35842177, 5159904769, 743009863681, 106993223294977, 15407021789577217, 2218611109320327169, 319479999401581608961, 46005119909741205651457, 6624737266953695061344257, 953962166440743626203987969

Offset

0,1

Comments

The corresponding left Aurifeuillian factor is A220989.

Links

Table of n, a(n) for n=0..12.

Wikipedia, Cunningham Project

Index entries for linear recurrences with constant coefficients, signature (157,-1884,1728).

Formula

Aurifeuillian factorization: 12^(6n+3) + 1 = (12^(2n+1) + 1) * A220989(n) * a(n).

G.f.: -(2736*x^2-1182*x+19) / ((x-1)*(12*x-1)*(144*x-1)). - Colin Barker, Jan 03 2013

Mathematica

Table[12^(2n+1) + 6 * 12^n + 1, {n, 0, 10}]
LinearRecurrence[{157, -1884, 1728}, {19, 1801, 249697}, 20] (* Harvey P. Dale, Mar 26 2022 *)

Prog

(PARI) a(n)=12^(2*n+1)+6*12^n+1 \\ Charles R Greathouse IV, Sep 28 2015

Crossrefs

Cf. A092440, A085601, A220978, A198410, A220979-A220989.

Sequence in context: A068748 A289736 A180394 * A098846 A116012 A203704

Adjacent sequences: A220987 A220988 A220989 * A220991 A220992 A220993

Keyword

nonn,easy

Author

Stuart Clary, Dec 27 2012

Status

approved