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A026565
a(n) = 6*a(n-2), starting with 1, 3, 9.
4
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
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
KEYWORD
nonn,easy
EXTENSIONS
Better name from Ralf Stephan, Jul 17 2013
STATUS
approved