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

0,5

Comments

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

Links

Table of n, a(n) for n=0..65.

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

Formula

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

Example

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;

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[%]

Crossrefs

Cf. A143214.

Sequence in context: A228053 A031262 A047072 * A260971 A053258 A350738

Adjacent sequences: A178055 A178056 A178057 * A178059 A178060 A178061

Keyword

nonn,tabl

Author

Roger L. Bagula, May 18 2010

Extensions

Edited by R. J. Mathar, Mar 10 2015

Status

approved