A143210 Triangle read by rows: Gray code of Eulerian(n,m), 1<=m<=n.

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

Offset: 1

Author

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

Keywords

• nonn
• tabl

Comments

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

Examples

			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;
		

Links

• Eric W. Weisstein, Gray Code

Crossrefs

Cf. A178059.

Programs

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[%]

Formula

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

Extensions

Edited by R. J. Mathar, Mar 10 2015