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

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, 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

Offset: 0

Author

Roger L. Bagula, May 18 2010

Keywords

• nonn
• tabl

Comments

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

Examples

			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, 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;
		

Links

• Eric W. Weisstein’s World of Mathematics, Gray code

Crossrefs

Cf. A143214.

Programs

Maple

A178058 := proc(n,m)
    A005811(binomial(n,m)) ;
end proc: # R. J. Mathar, Mar 10 2015

Mathematica

GrayCodeList[k_] := Module[{b = IntegerDigits[k, 2], i},
Do[
If[b[[i - 1]] == 1, b[[i]] = 1 - b[[i]]],
{i, Length[b], 2, -1}
];
b
]
Table[Table[Apply[Plus, GrayCodeList[Binomial[n, m]]], {m, 0, n}], {n, 0, 10}];
Flatten[%]

Formula

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

Extensions

Edited by R. J. Mathar, Mar 10 2015