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
Examples
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;
Links
- Eric W. Weisstein, Gray code
Programs
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Maple
A143261 := proc(n,m) binomial(n,m) ; A003188(%) ; A030101(%) ; end proc: # R. J. Mathar, Mar 10 2015
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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]
Formula
Extensions
Edited by R. J. Mathar, Mar 10 2015
Comments