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

Author

Stuart Clary, Dec 27 2012

Keywords

• nonn
• easy

Comments

The corresponding left Aurifeuillian factor is A220989.

Links

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

Crossrefs

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

Programs

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 *)

PARI

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

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