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A143210 Triangle read by rows: Gray code of Eulerian(n,m), 1<=m<=n. 1
1, 1, 1, 1, 6, 1, 1, 14, 14, 1, 1, 23, 99, 23, 1, 1, 37, 441, 441, 37, 1, 1, 68, 244, 456, 244, 68, 1, 1, 140, 167, 386, 386, 167, 140, 1, 1, 269, 408, 255, 785, 255, 408, 269, 1, 1, 527, 912, 788, 987, 987, 788, 912, 527, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

Row sums are: 1, 2, 8, 30, 147, 958, 1082, 1388, 2651, 6430,...

LINKS

Table of n, a(n) for n=1..55.

Eric W. Weisstein, Gray Code

FORMULA

T(n,m) = A003188(A008292(n,m)). - R. J. Mathar, Mar 10 2015

EXAMPLE

1;

1, 1;

1, 6, 1;

1, 14, 14, 1;

1, 23, 99, 23, 1;

1, 37, 441, 441, 37, 1;

1, 68, 244, 456, 244, 68, 1;

1, 140, 167, 386, 386, 167, 140, 1;

1, 269, 408, 255, 785, 255, 408, 269, 1;

1, 527, 912, 788, 987, 987, 788, 912, 527, 1;

MATHEMATICA

Code 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_] := f[x, n] = (1 - x)^(n + 1)*Sum[k^n*x^k, {k, 0, Infinity}]/x; Table[FullSimplify[ExpandAll[f[x, n]]], {n, 0, 10}]; a = Table[CoefficientList[FullSimplify[ExpandAll[f[x, n]]], x], {n, 1, 10}]; Table[Flatten[Table[GrayCode[a[[n]][[m]], 10], {m, 1, n}]], {n, 1, Length[ a]}]; Flatten[%]

CROSSREFS

Cf. A178059.

Sequence in context: A203956 A082105 A230073 * A205133 A152238 A295985

Adjacent sequences:  A143207 A143208 A143209 * A143211 A143212 A143213

KEYWORD

nonn,tabl

AUTHOR

Roger L. Bagula and Gary W. Adamson, Oct 20 2008

EXTENSIONS

Edited by R. J. Mathar, Mar 10 2015

STATUS

approved

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Last modified November 19 20:42 EST 2019. Contains 329323 sequences. (Running on oeis4.)