A152299 A threes sequence that gets more even factors out: a(n) = (3^n - 1)*(3^n + 1)/2^(4 - (n mod 2)).

0, 1, 5, 91, 410, 7381, 33215, 597871, 2690420, 48427561, 217924025, 3922632451, 17651846030, 317733228541, 1429799528435, 25736391511831, 115813761803240, 2084647712458321, 9380914706062445, 168856464709124011, 759854091191058050, 13677373641439044901

Offset

0,3

Links

Andrew Howroyd, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (0,82,0,-81).

Formula

a(n) = (3^n - 1)*(3^n + 1)/2^(4 - (n mod 2)).

From R. J. Mathar, Dec 04 2008: (Start)

a(n) = 82*a(n-2) - 81*a(n-4).

G.f.: x*(1 + 5*x + 9*x^2)/((1 - x)*(1-9*x)*(1 + x)*(1 + 9*x)). (End)

a(n) = A152258(n) / A002452(n) for n > 0. - Elmo R. Oliveira, May 12 2026

Mathematica

Clear[a, n];
a[n_] :=(3^n - 1)*(3^n + 1)/2^(4 - Mod[n, 2]);
Table[a[n], {n, 0, 30}]

Crossrefs

Cf. A002452, A003462, A152258.

Sequence in context: A158073 A038636 A282052 * A355371 A242945 A243198

Adjacent sequences: A152296 A152297 A152298 * A152300 A152301 A152302

Keyword

nonn,easy

Author

Roger L. Bagula, Dec 02 2008

Extensions

a(0) = 0 inserted by Andrew Howroyd, Oct 22 2025

Status

approved