A026565 a(n) = 6*a(n-2), starting with 1, 3, 9.

1, 3, 9, 18, 54, 108, 324, 648, 1944, 3888, 11664, 23328, 69984, 139968, 419904, 839808, 2519424, 5038848, 15116544, 30233088, 90699264, 181398528, 544195584, 1088391168, 3265173504, 6530347008, 19591041024, 39182082048

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (0,6).

Formula

a(n) = Sum_{j=0..2*n} A026552(n, j).

G.f.: (1+3*x+3*x^2)/(1-6*x^2). - Ralf Stephan, Feb 03 2004

a(0)=1, a(1)=3; a(n) = 3*a(n-1) if n is even, a(n) = 2*a(n-1) if n is odd. - Vincenzo Librandi, Nov 19 2010

a(n) = (1/4)*6^(n/2)*(3*(1+(-1)^n) + sqrt(6)*(1-(-1)^n)) - (1/2)*[n=0]. - G. C. Greubel, Dec 17 2021

Mathematica

Table[(1/4)*6^(n/2)*(3*(1+(-1)^n) + Sqrt[6]*(1-(-1)^n)) - (1/2)*Boole[n==0], {n, 0, 35}] (* G. C. Greubel, Dec 17 2021 *)

Prog

(Magma) [1] cat [n le 2 select 3^n else 6*Self(n-2): n in [1..35]]; // G. C. Greubel, Dec 17 2021
(Sage)
def A026565(n): return ( (3/2)*6^(n/2) if (n%2==0) else 3*6^((n-1)/2) ) - bool(n==0)/2
[A026565(n) for n in (0..30)] # G. C. Greubel, Dec 17 2021

Crossrefs

Cf. A026532, A026534, A026551, A026552, A026567.

Sequence in context: A056372 A181574 A101652 * A174470 A190905 A133136

Adjacent sequences: A026562 A026563 A026564 * A026566 A026567 A026568

Keyword

nonn,easy

Author

Clark Kimberling

Extensions

Better name from Ralf Stephan, Jul 17 2013

Status

approved