|
Search: id:A137696
|
|
|
| A137696 |
|
Triangular sequence of coefficients from a polynomial recursion: p(x,n)=p(x,Floor[(n-1)/2])-x^2*p(x,n-3)+x. |
|
+0
1
|
|
| 1, 0, 1, 0, 1, 1, 0, 2, -1, 0, 2, 0, -1, 0, 2, 1, -1, -1, 0, 2, 1, -2, 1, 0, 3, -1, -2, 0, 1, 0, 3, -1, -2, -1, 1, 1, 0, 3, 0, -3, -1, 2, -1, 0, 3, 0, -4, 1, 2, 0, -1
(list; table; graph; listen)
|
|
|
OFFSET
|
1,8
|
|
|
COMMENT
|
Row sums are: {1, 1, 2, 1, 1, 1, 2, 1, 1, 0, 1, ...}
|
|
FORMULA
|
p(x,n)=p(x,Floor[(n-1)/2])-x^2*p(x,n-3)+x; out_n,m=Coefficient(p(x,n)).
|
|
EXAMPLE
|
{1},
{0, 1},
{0, 1, 1},
{0, 2, -1},
{0, 2, 0, -1},
{0, 2, 1, -1, -1},
{0, 2, 1, -2, 1},
{0, 3, -1, -2, 0, 1},
{0, 3, -1, -2, -1,1, 1},
{0, 3, 0, -3, -1, 2, -1},
{0, 3, 0, -4, 1, 2, 0, -1}
|
|
MATHEMATICA
|
Clear[p, x]; p[x, -1] = 0; p[x, 0] = 1; p[x, 1] = x; p[x, 2] = x^2 + x; p[x_, n_] := p[x, n] = p[x, Floor[(n - 1)/2]] - x^2*p[x, n - 3] + x; Table[ExpandAll[p[x, n]], {n, 0, 10}]; a = Table[CoefficientList[p[x, n], x], {n, 0, 10}]; Flatten[a] Table[Apply[Plus, CoefficientList[p[x, n], x]], {n, 0, 10}];
|
|
CROSSREFS
|
Sequence in context: A033792 A033768 A033786 this_sequence A143614 A071412 A080884
Adjacent sequences: A137693 A137694 A137695 this_sequence A137697 A137698 A137699
|
|
KEYWORD
|
tabl,sign
|
|
AUTHOR
|
Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Apr 27 2008
|
|
|
Search completed in 0.002 seconds
|
