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A178059 Triangle read by rows: Number of 1's in the Gray code of Eulerian(n,m), 1<=m<=n.

%I A178059 #10 Aug 16 2020 07:54:15
%S A178059 1,1,1,1,2,1,1,3,3,1,1,4,4,4,1,1,3,6,6,3,1,1,2,7,6,7,2,1,1,3,7,5,5,7,
%T A178059 3,1,1,4,6,14,8,14,6,4,1,1,5,8,8,10,10,8,8,5,1,1,4,11,8,14,10,14,8,11,
%U A178059 4,1
%N A178059 Triangle read by rows: Number of 1's in the Gray code of Eulerian(n,m), 1<=m<=n.
%C A178059 Row sums are: 1, 2, 4, 8, 14, 20, 26, 32, 58, 64, 86,....
%H A178059 Eric W. Weisstein’s World of Mathematics, <a href="https://mathworld.wolfram.com/GrayCode.html">Gray Code</a>
%F A178059 T(n,m) = A005811(A008292(n,m)).
%e A178059 1;
%e A178059 1, 1;
%e A178059 1, 2, 1;
%e A178059 1, 3, 3, 1;
%e A178059 1, 4, 4, 4, 1;
%e A178059 1, 3, 6, 6, 3, 1;
%e A178059 1, 2, 7, 6, 7, 2, 1;
%e A178059 1, 3, 7, 5, 5, 7, 3, 1;
%e A178059 1, 4, 6, 14, 8, 14, 6, 4, 1;
%e A178059 1, 5, 8, 8, 10, 10, 8, 8, 5, 1;
%e A178059 1, 4, 11, 8, 14, 10, 14, 8, 11, 4, 1;
%t A178059 << DiscreteMath`Combinatorica`
%t A178059 GrayCodeList[k_] := Module[{b = IntegerDigits[k, 2], i},
%t A178059 Do[
%t A178059 If[b[[i - 1]] == 1, b[[i]] = 1 - b[[i]]],
%t A178059 {i, Length[b], 2, -1}
%t A178059 ];
%t A178059 b
%t A178059 ]
%t A178059 Table[Table[Apply[Plus, GrayCodeList[Eulerian[n+1, m]]], {m, 0, n}], {n, 0, 10}];
%t A178059 Flatten[%]
%K A178059 nonn,tabl
%O A178059 1,5
%A A178059 _Roger L. Bagula_, May 18 2010
%E A178059 Edited by _R. J. Mathar_, Mar 10 2015