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Trisection a(n) = A000265(3n).
1

%I #26 Aug 30 2024 06:24:05

%S 3,3,9,3,15,9,21,3,27,15,33,9,39,21,45,3,51,27,57,15,63,33,69,9,75,39,

%T 81,21,87,45,93,3,99,51,105,27,111,57,117,15,123,63,129,33,135,69,141,

%U 9,147,75,153,39,159,81,165,21,171,87,177,45,183,93,189,3,195,99,201,51

%N Trisection a(n) = A000265(3n).

%C The other trisections are A067745 and A075677.

%H G. C. Greubel, <a href="/A166466/b166466.txt">Table of n, a(n) for n = 1..10000</a>

%F A000265(A007283(n)) = 3. a(A007283(n)) = 9.

%F a(n) = 3*A000265(n).

%F Sum_{k=1..n} a(k) ~ n^2. - _Amiram Eldar_, Aug 30 2024

%p A166468 := proc(n) A000265(3*n) ; end: seq(A166468(n),n=1..80) ; # _R. J. Mathar_, Oct 21 2009

%t A166466[n_]:= If[n==0, 0, 3*n/2^IntegerExponent[n, 2]];

%t Table[A166466[n], {n,100}] (* based on Michael Somos's code of A000265 *) (* _G. C. Greubel_, Jul 31 2024 *)

%o (Magma)

%o A166466:= func< n | 3*n/2^Valuation(n,2) >;

%o [A166466(n): n in [1..120]]; // _G. C. Greubel_, Jul 31 2024

%o (SageMath)

%o def A166466(n): return 3*n//2^valuation(n,2)

%o [A166466(n) for n in (1..121)] # _G. C. Greubel_, Jul 31 2024

%o (PARI) a(n)=3*n>>valuation(n,2);

%o vector(100,n,a(n)) \\ _Joerg Arndt_, Aug 01 2024

%Y Cf. A000265, A007283, A067745, A075677.

%K nonn,easy

%O 1,1

%A _Paul Curtz_, Oct 14 2009

%E Comments turned into formulas by _R. J. Mathar_, Oct 21 2009