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, 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

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