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Search: id:A143261
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| A143261 |
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Sequence of sum of Gray code Binary digits for Pascal's triangle sequence : t(n,m)=GrayCodeBinarySum[Binomial[n,m]). |
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+0
1
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| 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
(list; graph; listen)
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OFFSET
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1,5
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COMMENT
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The result here is different than the Gray Code base ten result:
all the elements are odd: modulo two they would be ones.
Row sums are:
{1, 2, 5, 4, 13, 46, 29, 104, 127, 334, 683, 2104}.
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REFERENCES
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Weisstein, Eric W. "Gray Code." http : // mathworld.wolfram.com/GrayCode.html
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FORMULA
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t(n,m)=GrayCodeBinarySum[Binomial[n,m]).
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EXAMPLE
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{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}
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MATHEMATICA
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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]
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CROSSREFS
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Cf. A098957.
Sequence in context: A001165 A137420 A134866 this_sequence A093421 A146531 A030381
Adjacent sequences: A143258 A143259 A143260 this_sequence A143262 A143263 A143264
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KEYWORD
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nonn,uned,probation
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AUTHOR
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Roger L. Bagula and Gary W. Adamson (rlbagulatftn(AT)yahoo.com), Oct 21 2008
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