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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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified December 13 06:26 EST 2019. Contains 329968 sequences. (Running on oeis4.)