A220989 a(n) = 12^(2n+1) - 6 * 12^n + 1: the left Aurifeuillian factor of 12^(6n+3) + 1.

7, 1657, 247969, 35821441, 5159655937, 743006877697, 106993187463169, 15407021359595521, 2218611104160546817, 319479999339664244737, 46005119908998197280769, 6624737266944778960896001, 953962166440636632998608897

Offset: 0

Author

Stuart Clary, Dec 27 2012

Keywords

• nonn
• easy

Comments

The corresponding right Aurifeuillian factor is A220990.

Links

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

Crossrefs

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

Programs

Mathematica

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

Formula

Aurifeuillian factorization: 12^(6n+3) + 1 = (12^(2n+1) + 1) * a(n) * A220990(n).

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