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

%I #12 Sep 08 2022 08:46:05

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

%C This is the 2-adic valuation of A000930.

%H G. C. Greubel, <a href="/A227834/b227834.txt">Table of n, a(n) for n = 0..5000</a>

%t A000930[n_] := Sum[Binomial[n - 2*i, i], {i, 0, Floor[n/3]}];

%t Table[IntegerExponent[A000930[n], 2], {n, 0, 100}] (* _G. C. Greubel_, Apr 26 2017 *)

%o (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 Cf. A000930, A007814, A227835.

%K nonn

%O 0,6

%A _N. J. A. Sloane_, Aug 04 2013