A178058 - OEIS

%I #10 Aug 16 2020 07:55:27

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

%C Row sums are: 1, 2, 4, 4, 8, 16, 12, 20, 18, 32, 38,....

%H Eric W. Weisstein’s World of Mathematics, <a href="https://mathworld.wolfram.com/GrayCode.html">Gray code</a>

%F T(n,m) = A005811(binomial(n,m)), 0<=m<=n.

%e 1;

%e 1, 1;

%e 1, 2, 1;

%e 1, 1, 1, 1;

%e 1, 2, 2, 2, 1;

%e 1, 3, 4, 4, 3, 1;

%e 1, 2, 1, 4, 1, 2, 1;

%e 1, 1, 5, 3, 3, 5, 1, 1;

%e 1, 2, 2, 2, 4, 2, 2, 2, 1;

%e 1, 3, 4, 6, 2, 2, 6, 4, 3, 1;

%e 1, 4, 5, 2, 6, 2, 6, 2, 5, 4, 1;

%p A178058 := proc(n,m)

%p     A005811(binomial(n,m)) ;

%p end proc: # _R. J. Mathar_, Mar 10 2015

%t GrayCodeList[k_] := Module[{b = IntegerDigits[k, 2], i},

%t Do[

%t If[b[[i - 1]] == 1, b[[i]] = 1 - b[[i]]],

%t {i, Length[b], 2, -1}

%t ];

%t b

%t ]

%t Table[Table[Apply[Plus, GrayCodeList[Binomial[n, m]]], {m, 0, n}], {n, 0, 10}];

%t Flatten[%]

%Y Cf. A143214.

%K nonn,tabl

%O 0,5

%A _Roger L. Bagula_, May 18 2010

%E Edited by _R. J. Mathar_, Mar 10 2015