|
| |
|
|
A146565
|
|
A double offset polynomial as a triangle of coefficients: p(x,n)=(x + 1)^n + If[n >= 2, x^2*(x + 1)^(n - 1), x^(n + 1)] + If[n >= 4, x^2*(x + 1)^(n - 3), 0].
|
|
0
|
|
|
|
1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 3, 4, 3, 1, 1, 4, 8, 8, 4, 1, 1, 5, 12, 16, 12, 5, 1, 1, 6, 17, 28, 28, 17, 6, 1, 1, 7, 23, 45, 56, 45, 23, 7, 1, 1, 8, 30, 68, 101, 101, 68, 30, 8, 1, 1, 9, 38, 98, 169, 202, 169, 98, 38, 9, 1, 1, 10, 47, 136, 267, 371, 371, 267, 136, 47, 10, 1
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,7
|
|
|
COMMENTS
|
Row sums are:{2, 3, 6, 12, 26, 52, 104, 208, 416, 832, 1664}.
|
|
|
LINKS
|
Table of n, a(n) for n=0..76.
|
|
|
FORMULA
|
p(x,n)=(x + 1)^n + If[n >= 2, x^2*(x + 1)^(n - 1), x^(n + 1)] + If[n >= 4, x^2*(x + 1)^(n - 3), 0]; t(n,m)=Coefficients(p(x,n)).
|
|
|
EXAMPLE
|
{1, 1}, {1, 1, 1}, {1, 2, 2, 1}, {1, 3, 4, 3, 1}, {1, 4, 8, 8, 4, 1}, {1, 5, 12, 16, 12, 5, 1}, {1, 6, 17, 28, 28, 17, 6, 1}, {1, 7, 23, 45, 56, 45, 23, 7, 1}, {1, 8, 30, 68, 101, 101, 68, 30, 8, 1}, {1, 9, 38, 98, 169, 202, 169, 98, 38, 9, 1}, {1, 10, 47, 136, 267, 371, 371, 267, 136, 47, 10, 1}
|
|
|
MATHEMATICA
|
p[x_, n_] = (x + 1)^n + If[n >= 2, x^2*(x + 1)^(n - 1), x^(n + 1)] + If[n >= 4, x^2*(x + 1)^(n - 3), 0]; Table[CoefficientList[p[x, n], x], {n, 0, 10}]; Flatten[%]
|
|
|
CROSSREFS
|
A072405
Sequence in context: A047089 A122218 A072405 * A115594 A086623 A034928
Adjacent sequences: A146562 A146563 A146564 * A146566 A146567 A146568
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
Roger L. Bagula, Nov 01 2008
|
|
|
STATUS
|
approved
|
| |
|
|
