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A141398 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]. 0
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; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

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]

REFERENCES

R. N. Cahn, Semi-Simple Lie Algebras and Their Representations, Dover, NY, 2006, ISBN 0-486-44999-8, p. 139.

LINKS

Table of n, a(n) for n=1..55.

FORMULA

k=5; t(n,m,k)=Ceiling[((n - m)^k*(m + 1)^k - 2^(n - 1))/n^k].

EXAMPLE

{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}

MATHEMATICA

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]

CROSSREFS

Cf. A003991.

Sequence in context: A078181 A054110 A132048 * A058281 A046583 A046579

Adjacent sequences:  A141395 A141396 A141397 * A141399 A141400 A141401

KEYWORD

nonn,uned,tabl

AUTHOR

Roger L. Bagula, Aug 03 2008

STATUS

approved

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Last modified July 18 07:46 EDT 2019. Contains 325136 sequences. (Running on oeis4.)