A220981 a(n) = 6^(4n+2) - 6^(3n+2) + 3 * 6^(2n+1) - 6^(n+1) + 1: the left Aurifeuillian factor of 6^(12n+6) + 1.

13, 39493, 58809673, 78002205553, 101481622729633, 131604778271166913, 170578072060319947393, 221073129991920857571073, 286511629376393032228157953, 371319255900007820952456748033, 481229795439713382306649129101313

Offset: 0

Author

Stuart Clary, Dec 27 2012

Keywords

• nonn
• easy

Comments

The corresponding right Aurifeuillian factor is A220982.

Links

• Wikipedia, Cunningham Project
• Index entries for linear recurrences with constant coefficients, signature (1555,-345210,12427560,-72550080,60466176).

Crossrefs

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

Programs

Mathematica

Table[6^(4n+2) - 6^(3n+2) + 3 * 6^(2n+1) - 6^(n+1) + 1, {n, 0, 20}]
LinearRecurrence[{1555,-345210,12427560,-72550080,60466176},{13,39493,58809673,78002205553,101481622729633},20] (* Harvey P. Dale, Oct 01 2021 *)

Formula

Aurifeuillian factorization: 6^(12n+6) + 1 = (6^(4n+2) + 1) * a(n) * A220982(n).

G.f.: -(21835008*x^4+24984288*x^3+1885788*x^2+19278*x+13) / ((x-1)*(6*x-1)*(36*x-1)*(216*x-1)*(1296*x-1)). [Colin Barker, Jan 03 2013]