

A178059


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


1



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, 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, 4, 1
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OFFSET

1,5


COMMENTS

Row sums are: 1, 2, 4, 8, 14, 20, 26, 32, 58, 64, 86,....


LINKS

Table of n, a(n) for n=1..66.
Eric W. Weisstein, Gray Code


FORMULA

T(n,m) = A005811(A008292(n,m)).


EXAMPLE

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, 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, 4, 1;


MATHEMATICA

<< DiscreteMath`Combinatorica`
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
]
Table[Table[Apply[Plus, GrayCodeList[Eulerian[n+1, m]]], {m, 0, n}], {n, 0, 10}];
Flatten[%]


CROSSREFS

Sequence in context: A082905 A141524 A192650 * A116188 A318274 A049695
Adjacent sequences: A178056 A178057 A178058 * A178060 A178061 A178062


KEYWORD

nonn,tabl


AUTHOR

Roger L. Bagula, May 18 2010


EXTENSIONS

Edited by R. J. Mathar, Mar 10 2015


STATUS

approved



