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A143261
Triangle read by rows: binary reversed Gray code of binomial(n,m).
1
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
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
Sequence in context: A137420 A134866 A340085 * A204116 A093421 A146531
KEYWORD
nonn,tabl
AUTHOR
EXTENSIONS
Edited by R. J. Mathar, Mar 10 2015
STATUS
approved