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.
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
KEYWORD
AUTHOR
Roger L. Bagula, Aug 03 2008
STATUS
approved