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

0,1

Comments

The corresponding right Aurifeuillian factor is A220982.

Links

Table of n, a(n) for n=0..10.

Wikipedia, Cunningham Project

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

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]

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 *)

Crossrefs

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

Sequence in context: A013752 A076811 A203691 * A258670 A375538 A048917

Adjacent sequences: A220978 A220979 A220980 * A220982 A220983 A220984

Keyword

nonn,easy

Author

Stuart Clary, Dec 27 2012

Status

approved