A143261 Triangle read by rows: binary reversed Gray code of binomial(n,m).

1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 3, 5, 3, 1, 1, 7, 15, 15, 7, 1, 1, 5, 1, 15, 1, 5, 1, 1, 1, 31, 19, 19, 31, 1, 1, 1, 3, 9, 9, 83, 9, 9, 3, 1, 1, 11, 27, 63, 65, 65, 63, 27, 11, 1, 1, 15, 55, 17, 221, 65, 221, 17, 55, 15, 1, 1, 7, 13, 239, 495, 297, 297, 495, 239, 13, 7, 1

Offset

0,5

Comments

Row sums are: 1, 2, 5, 4, 13, 46, 29, 104, 127, 334, 683, 2104,...

Links

Table of n, a(n) for n=0..77.

Eric W. Weisstein, Gray code

Formula

T(n,m) = A030101(A003188(binomial(n,m)) = A030101(A143214(n,m)). - R. J. Mathar, Mar 10 2015

Example

1;
1, 1;
1, 3, 1;
1, 1, 1, 1;
1, 3, 5, 3, 1;
1, 7, 15, 15, 7, 1;
1, 5, 1, 15, 1, 5, 1;
1, 1, 31, 19, 19, 31, 1, 1;
1, 3, 9, 9, 83, 9, 9, 3, 1;
1, 11, 27, 63, 65, 65, 63, 27, 11, 1;
1, 15, 55, 17, 221, 65, 221, 17, 55, 15, 1;
1, 7, 13, 239, 495, 297, 297, 495, 239, 13, 7, 1;

Maple

A143261 := proc(n, m)
    binomial(n, m) ;
    A003188(%) ;
    A030101(%) ;
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 ]; b = Table[Table[Sum[GrayCodeList[Binomial[n, k]][[m + 1]]*2^m, {m, 0, Length[GrayCodeList[Binomial[n, k]]] - 1}], {k, 0, n}], {n, 0, Length[a]}]; Flatten[b]

Crossrefs

Cf. A143214, A178058.

Sequence in context: A137420 A134866 A340085 * A204116 A093421 A146531

Adjacent sequences: A143258 A143259 A143260 * A143262 A143263 A143264

Keyword

nonn,tabl

Author

Roger L. Bagula and Gary W. Adamson, Oct 21 2008

Extensions

Edited by R. J. Mathar, Mar 10 2015

Status

approved