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A227834 2^a(n) is the highest power of 2 dividing A000930(n).

%I A227834 #12 Sep 08 2022 08:46:05
%S A227834 0,0,0,1,0,2,1,0,0,0,2,0,2,3,0,0,0,1,0,3,1,0,0,0,3,0,3,7,0,0,0,1,0,2,
%T A227834 1,0,0,0,2,0,2,3,0,0,0,1,0,4,1,0,0,0,4,0,4,6,0,0,0,1,0,2,1,0,0,0,2,0,
%U A227834 2,3,0,0,0,1,0,3,1,0,0,0,3,0,3,6,0,0,0,1,0,2,1,0,0,0,2,0,2,3,0,0,0,1,0,5,1,0,0,0,5,0,5,7,0
%N A227834 2^a(n) is the highest power of 2 dividing A000930(n).
%C A227834 This is the 2-adic valuation of A000930.
%H A227834 G. C. Greubel, <a href="/A227834/b227834.txt">Table of n, a(n) for n = 0..5000</a>
%t A227834 A000930[n_] := Sum[Binomial[n - 2*i, i], {i, 0, Floor[n/3]}];
%t A227834 Table[IntegerExponent[A000930[n], 2], {n, 0, 100}] (* _G. C. Greubel_, Apr 26 2017 *)
%o A227834 (Magma) A000930:=func<i | &+[Binomial(i-2*k,k): k in [0..i div 3]]>; [Valuation(A000930(n),2): n in [0..120]]; // _Bruno Berselli_, Aug 05 2013
%Y A227834 Cf. A000930, A007814, A227835.
%K A227834 nonn
%O A227834 0,6
%A A227834 _N. J. A. Sloane_, Aug 04 2013