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 A143213 Triangle T(n,m) read by rows: Gray code of A060187(n,m) (decimal representation), 1<=m<=n. 0
 1, 1, 1, 1, 5, 1, 1, 28, 28, 1, 1, 106, 149, 106, 1, 1, 155, 987, 987, 155, 1, 1, 955, 440, 514, 440, 955, 1, 1, 194, 137, 974, 974, 137, 194, 1, 1, 340, 754, 60, 293, 60, 754, 340, 1, 1, 181, 238, 166, 377, 377, 166, 238, 181, 1, 1, 977, 283, 540, 411, 142, 411, 540 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS Row sums are 1, 2, 7, 58, 363, 2286, 3306, 2612, 2603, 1926, 4566,... LINKS Eric Weisstein, Mathematica Notebook GrayCode.nb Eric Weisstein, Gray Code, MathWorld. FORMULA T(n,m) = A003188(A060187(n,m)). - R. J. Mathar, Nov 11 2011 EXAMPLE 1; 1, 1; 1, 5, 1; 1, 28, 28, 1; 1, 106, 149, 106, 1; 1, 155, 987, 987, 155, 1; 1, 955, 440, 514, 440, 955, 1; 1, 194, 137, 974, 974, 137, 194, 1; 1, 340, 754, 60, 293, 60, 754, 340, 1; 1, 181, 238, 166, 377, 377, 166, 238, 181, 1; 1, 977, 283, 540, 411, 142, 411, 540, 283, 977, 1; 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 ]; FromGrayCodeList[d_] := Module[{b = d, i, j}, Do[ If[Mod[Sum[b[[j]], {j, i - 1}], 2] == 1, b[[i]] = 1 - b[[i]]], {i, n = Length[d], 2, -1} ]; FromDigits[b, 2] ]; GrayCode[i_, n_] := FromDigits[BitXor @@@ Partition[Prepend[ IntegerDigits[i, 2, n], 0], 2, 1], 2] FromGrayCode[i_, n_] := FromDigits[BitXor[IntegerDigits[i, 2, n], FoldList[ BitXor, 0, Most[IntegerDigits[i, 2, n]]]], 2]; Clear[f, a, n, m, x]; (*A123125*) f[x_, n_] :=2^n*(1 - x)^(1 + n)*LerchPhi[x, -n, 1/2]; Table[FullSimplify[ExpandAll[f[x, n]]], {n, 0, 10}]; a = Table[CoefficientList[FullSimplify[ExpandAll[f[x, n]]], x], {n, 1, 10}]; b=Table[Flatten[Table[GrayCode[a[[n]][[m]], 10], {m, 1, n}]], {n, 1, Length[ a]}]; Flatten[%] CROSSREFS Cf. A060187. Sequence in context: A176793 A118190 A172342 * A172377 A156587 A058720 Adjacent sequences:  A143210 A143211 A143212 * A143214 A143215 A143216 KEYWORD nonn,tabl AUTHOR Roger L. Bagula and Gary W. Adamson, Oct 20 2008 STATUS approved

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Last modified December 11 01:07 EST 2019. Contains 329910 sequences. (Running on oeis4.)