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
Links
- G. C. Greubel, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (0,6).
Programs
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Magma
[1] cat [n le 2 select 3^n else 6*Self(n-2): n in [1..35]]; // G. C. Greubel, Dec 17 2021
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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 *) -
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
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
Extensions
Better name from Ralf Stephan, Jul 17 2013