A220978 a(n) = 3^(2*n+1) - 3^(n+1) + 1: The left Aurifeuillian factor of 3^(6*n+3) + 1.

1, 19, 217, 2107, 19441, 176419, 1592137, 14342347, 129120481, 1162202419, 10460176057, 94142647387, 847287015121, 7625592702019, 68630363015977, 617673353237227, 5559060437415361, 50031544711579219, 450283904728735897, 4052555149532191867

Offset: 0

Author

Stuart Clary, Dec 27 2012

Keywords

• nonn
• easy

Comments

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

Links

• Wikipedia, Cunningham Project
• Index entries for linear recurrences with constant coefficients, signature (13, -39, 27).

Crossrefs

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

Programs

Mathematica

Table[3^(2n+1) - 3^(n+1) + 1, {n, 0, 30}]
LinearRecurrence[{13,-39,27},{1,19,217},30] (* Harvey P. Dale, Mar 17 2013 *)

PARI

Vec((1 + 3*x)^2/((1 - x)*(1 - 3*x)*(1 - 9*x)) + O(x^30)) \\ Michel Marcus, Feb 12 2015

Formula

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

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