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A178058 Number of 1's in the Gray code for binomial(n,m).

%I A178058 #10 Aug 16 2020 07:55:27
%S A178058 1,1,1,1,2,1,1,1,1,1,1,2,2,2,1,1,3,4,4,3,1,1,2,1,4,1,2,1,1,1,5,3,3,5,
%T A178058 1,1,1,2,2,2,4,2,2,2,1,1,3,4,6,2,2,6,4,3,1,1,4,5,2,6,2,6,2,5,4,1
%N A178058 Number of 1's in the Gray code for binomial(n,m).
%C A178058 Row sums are: 1, 2, 4, 4, 8, 16, 12, 20, 18, 32, 38,....
%H A178058 Eric W. Weisstein’s World of Mathematics, <a href="https://mathworld.wolfram.com/GrayCode.html">Gray code</a>
%F A178058 T(n,m) = A005811(binomial(n,m)), 0<=m<=n.
%e A178058 1;
%e A178058 1, 1;
%e A178058 1, 2, 1;
%e A178058 1, 1, 1, 1;
%e A178058 1, 2, 2, 2, 1;
%e A178058 1, 3, 4, 4, 3, 1;
%e A178058 1, 2, 1, 4, 1, 2, 1;
%e A178058 1, 1, 5, 3, 3, 5, 1, 1;
%e A178058 1, 2, 2, 2, 4, 2, 2, 2, 1;
%e A178058 1, 3, 4, 6, 2, 2, 6, 4, 3, 1;
%e A178058 1, 4, 5, 2, 6, 2, 6, 2, 5, 4, 1;
%p A178058 A178058 := proc(n,m)
%p A178058     A005811(binomial(n,m)) ;
%p A178058 end proc: # _R. J. Mathar_, Mar 10 2015
%t A178058 GrayCodeList[k_] := Module[{b = IntegerDigits[k, 2], i},
%t A178058 Do[
%t A178058 If[b[[i - 1]] == 1, b[[i]] = 1 - b[[i]]],
%t A178058 {i, Length[b], 2, -1}
%t A178058 ];
%t A178058 b
%t A178058 ]
%t A178058 Table[Table[Apply[Plus, GrayCodeList[Binomial[n, m]]], {m, 0, n}], {n, 0, 10}];
%t A178058 Flatten[%]
%Y A178058 Cf. A143214.
%K A178058 nonn,tabl
%O A178058 0,5
%A A178058 _Roger L. Bagula_, May 18 2010
%E A178058 Edited by _R. J. Mathar_, Mar 10 2015