|
| |
|
|
A155123
|
|
Six levels of the coefficient triangle of the Pascal-Sierpinski functions.
|
|
1
|
|
|
|
1, 2, 2, 2, 0, 4, 4, 0, -4, 8, 12, 0, 8, -32, 8, 48
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,2
|
|
|
COMMENTS
|
Row sums are 2^(n+1);
{1, 2, 4, 8, 16, 32,...}.
|
|
|
LINKS
|
Table of n, a(n) for n=0..15.
|
|
|
FORMULA
|
Triangle:
{{1},
{1, 1},
{1, 2*n, 1},
{1, f[n], f[n], 1},
{1, g[n], 6 + 24 *(n - 1) + 28*(n - 1)^2 + 8* ( n - 1)^3, g[n], 1},
{1, h[n], k[n - 1] - h[n] - 1, k[n - 1] - h[n] - 1, h[n], 1}}
f[n_]=3*n^2 - (n - 1)^2;
g[n_]=-2 + 2 *n + 2* n^2 + 2 n^3;
h[n_]=-3 + 2 n + 2 n^2 + 2 n^3 + 2*n^4;
k[n_]=16+ 80 n + 140 *n^2 + 100*n^3 + 24* n^4;
These functions and the triangles they make are general Pascal-Sierpinski
functions.
|
|
|
EXAMPLE
|
{1},
{2},
{2, 2},
{0, 4, 4},
{0, -4, 8, 12},
{0, 8, -32, 8, 48}
|
|
|
MATHEMATICA
|
a1 = {{1},
{1, 1},
{1, 2 *n, 1},
{1, -1 + 2 *n + 2 n^2, -1 + 2 n + 2 n^2, 1},
{1, -2 + 2 *n + 2 n^2 + 2 n^3, 2 - 8 n + 4 n^2 + 8 n^3, -2 + 2* n + 2 n^2 + 2 n^3, 1},
{1, -3 + 2 n + 2 n^2 + 2 n^3 + 2 n^4, 2 + 2 n - 18 n^2 + 2 n^3 + 22 n^4, 2 + 2 n - 18 n^2 + 2 n^3 + 22 n^4, -3 + 2 n + 2 n^2 + 2 n^3 + 2 n^4, 1}}
Table[CoefficientList[Apply[Plus, a1[[m]]], n], {m, 1, Length[a1]}];
Flatten[%]
|
|
|
CROSSREFS
|
A142463
Sequence in context: A263527 A261444 A000091 * A125938 A215461 A158851
Adjacent sequences: A155120 A155121 A155122 * A155124 A155125 A155126
|
|
|
KEYWORD
|
tabl,uned,sign
|
|
|
AUTHOR
|
Roger L. Bagula, Jan 20 2009
|
|
|
STATUS
|
approved
|
| |
|
|
