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Search: id:A141398
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| A141398 |
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The fifth power ( k=5) of the normalized neo-combinations: t(n,m,k)=Ceiling[((n - m)^k*(m + 1)^k - 2^(n - 1))/n^k]. |
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+0
1
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| 0, 1, 1, 1, 5, 1, 1, 8, 8, 1, 1, 11, 19, 11, 1, 1, 13, 32, 32, 13, 1, 1, 15, 46, 63, 46, 15, 1, 1, 17, 58, 98, 98, 58, 17, 1, 1, 18, 70, 135, 166, 135, 70, 18, 1, 1, 19, 80, 173, 243, 243, 173, 80, 19, 1
(list; table; graph; listen)
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OFFSET
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1,5
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COMMENT
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Row sums are:
{0, 2, 7, 18, 43, 92, 187, 348, 614, 1032};
This version is designed to "look like"
a Pascal's triangle.
The fractal picture is given by:
Clear[T, n, m, a];
T[n_, m_] = Ceiling[((n - m)^5*(m + 1)^5 - 2^(n - 1))/n^5];
a = Table[Table[T[n, m], {m, 0, n - 1}], {n, 1, 100}];
f[n_] := Table[0, {i, 1, n}];
b = Table[Join[Mod[a[[n]], 2], f[Length[a] - n]], {n, 2, Length[a] - 1}];
ListDensityPlot[b, Mesh -> False]
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REFERENCES
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R. N. Cahn, Semi-Simple Lie Algebras and Their Representations, Dover, NY, 2006, ISBN 0-486-44999-8, p. 139.
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FORMULA
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k=5; t(n,m,k)=Ceiling[((n - m)^k*(m + 1)^k - 2^(n - 1))/n^k].
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EXAMPLE
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{0},
{1, 1},
{1, 5, 1},
{1, 8, 8, 1},
{1, 11, 19, 11, 1},
{1, 13, 32, 32, 13, 1},
{1, 15, 46, 63, 46, 15, 1},
{1, 17, 58, 98, 98, 58, 17, 1},
{1, 18, 70, 135, 166, 135, 70, 18, 1},
{1, 19, 80, 173, 243, 243, 173, 80, 19, 1}
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MATHEMATICA
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Clear[T, n, m, a] k = 5; T[n_, m_] = Ceiling[((n - m)^k*(m + 1)^k - 2^(n - 1))/n^k]; a = Table[Table[T[n, m], {m, 0, n - 1}], {n, 1, 10}]; Flatten[a]
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CROSSREFS
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Cf. A003991.
Sequence in context: A078181 A054110 A132048 this_sequence A058281 A046583 A046579
Adjacent sequences: A141395 A141396 A141397 this_sequence A141399 A141400 A141401
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KEYWORD
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nonn,uned,tabl
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Aug 03 2008
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