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%I #14 Sep 08 2022 08:46:05
%S 0,0,0,0,1,1,0,0,0,0,1,2,3,5,5,3,2,1,0,0,0,0,1,1,0,0,0,0,1,2,3,5,6,6,
%T 7,8,9,11,13,15,18,18,15,13,11,9,8,7,6,6,5,3,2,1,0,0,0,0,1,1,0,0,0,0,
%U 1,2,3,5,5,3,2,1,0,0,0,0,1,1,0,0,0,0,1,2,3,5,6,6,7,8,9,11,13,15,18,19,18,18,18,18,19
%N 3-adic valuation of A005130(n).
%C 3^a(n) is the highest power of 3 dividing A005130(n).
%H Amiram Eldar, <a href="/A227833/b227833.txt">Table of n, a(n) for n = 0..10000</a>
%F From _Amiram Eldar_, Feb 21 2021: (Start)
%F a(n) = A007949(A005130(n)).
%F a(n) = a(n-1) + (s(2*n-2) + s(2*n-1) - s(n-1) - s(3*n-2))/2, where s(n) = A053735(n). (End)
%t s[n_] := Plus @@ IntegerDigits[n, 3]; a[0] = 0; a[n_] := a[n] = a[n - 1] + (s[2*n - 2] + s[2*n - 1] - s[n - 1] - s[3*n - 2])/2; Array[a, 101, 0] (* _Amiram Eldar_, Feb 21 2021 *)
%o (Magma) A005130:=func<i | IsZero(i) select 1 else &*[Factorial(3*k+1)/Factorial(i+k): k in [0..i-1]]>; [Valuation(A005130(n),3): n in [0..100]]; // _Bruno Berselli_, Aug 05 2013
%Y Cf. A005130, A007949, A053735, A194827.
%K nonn
%O 0,12
%A _N. J. A. Sloane_, Aug 04 2013, based on a suggestion from Victor H. Moll.
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