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A157603
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Combinatorial long tail mean collapse of A055248: t(n,m) =1 if greater than the row mean of A055248 else A055248.
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1, 1, 1, 1, 3, 1, 1, 1, 4, 1, 1, 1, 11, 5, 1, 1, 1, 1, 16, 6, 1, 1, 1, 1, 42, 22, 7, 1, 1, 1, 1, 1, 64, 29, 8, 1, 1, 1, 1, 1, 163, 93, 37, 9, 1, 1, 1, 1, 1, 1, 256, 130, 46, 10, 1, 1, 1, 1, 1, 1, 638, 386, 176, 56, 11, 1
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| Row sums are:
{1, 2, 5, 7, 19, 26, 75, 106, 307, 448, 1273,...}.
This kind of function comes from Per Bak's sand pile theory
applied to a long tail combinatorial function like A055248.
The idea is that the heavy mean or larger values collapse to the baseline one.
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FORMULA
| t(n,m) =1 if A055248 than the row mean of A055248 else A055248.
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EXAMPLE
| {1},
{1, 1},
{1, 3, 1},
{1, 1, 4, 1},
{1, 1, 11, 5, 1},
{1, 1, 1, 16, 6, 1},
{1, 1, 1, 42, 22, 7, 1},
{1, 1, 1, 1, 64, 29, 8, 1},
{1, 1, 1, 1, 163, 93, 37, 9, 1},
{1, 1, 1, 1, 1, 256, 130, 46, 10, 1},
{1, 1, 1, 1, 1, 638, 386, 176, 56, 11, 1}
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MATHEMATICA
| t[n_, m_] = Sum[Binomial[n, m - k], {k, 0, m}];
a = Table[Table[If[t[n, m] <= Sum[t[n, m], {m, 0, n}]/( n + 1), 1, t[n, n - m]], {m, 0, n}], {n, 0, 10}];
Flatten[%]
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CROSSREFS
| Sequence in context: A157261 A079110 A079619 * A059619 A098950 A123940
Adjacent sequences: A157600 A157601 A157602 * A157604 A157605 A157606
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KEYWORD
| nonn,tabl
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AUTHOR
| Roger L. Bagula and Gary W. Adamson (rlbagulatftn(AT)yahoo.com), Mar 02 2009
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