|
Search: id:A108520
|
|
|
| A108520 |
|
Expansion of 1/(1+2*x+2*x^2). |
|
+0
7
|
|
| 1, -2, 2, 0, -4, 8, -8, 0, 16, -32, 32, 0, -64, 128, -128, 0, 256, -512, 512, 0, -1024, 2048, -2048, 0, 4096, -8192, 8192, 0, -16384, 32768, -32768, 0, 65536, -131072, 131072, 0, -262144, 524288, -524288, 0, 1048576, -2097152, 2097152, 0, -4194304, 8388608, -8388608
(list; graph; listen)
|
|
|
OFFSET
|
0,2
|
|
|
COMMENT
|
Yet another variation on A009545.
|
|
FORMULA
|
G.f.: 1/(1+2*x+2*x^2). E.g.f.: exp(-x)(cos(x)-sin(x)). a(n)=-2(a(n-1)+a(n-2)).
a(n)=sum{k=0..n, sum{j=0..n-k, C(k,j)C(k,n-j)(-2)^(n-j)}} - Paul Barry (pbarry(AT)wit.ie), Mar 09 2006
|
|
PROGRAM
|
(PARI) a(n)=if(n<0, 0, polcoeff(1/(1+2*x+2*x^2)+x*O(x^n), n))
(PARI) a(n)=if(n<1, n==0, -polsym(2+2*x+x^2, n-1)[n])
|
|
CROSSREFS
|
Cf. a(n)=(-1)^n A099087(n). a(n)=-A084102(n) if n>0.
Adjacent sequences: A108517 A108518 A108519 this_sequence A108521 A108522 A108523
Sequence in context: A086882 A100240 A072690 this_sequence A099087 A009545 A084102
|
|
KEYWORD
|
sign
|
|
AUTHOR
|
Michael Somos, Jun 07 2005
|
|
|
Search completed in 0.002 seconds
|
