|
Search: id:A105371
|
|
|
| A105371 |
|
Expansion of (1-x)(1-x+x^2)/(1-3x+4x^2-2x^3+x^4). |
|
+0
4
|
|
| 1, 1, 1, 0, -3, -8, -13, -13, 0, 34, 89, 144, 144, 0, -377, -987, -1597, -1597, 0, 4181, 10946, 17711, 17711, 0, -46368, -121393, -196418, -196418, 0, 514229, 1346269, 2178309, 2178309, 0, -5702887, -14930352, -24157817, -24157817, 0, 63245986, 165580141
(list; graph; listen)
|
|
|
OFFSET
|
0,5
|
|
|
COMMENT
|
Binomial transform of A105367.
|
|
LINKS
|
Index entries for two-way infinite sequences
|
|
FORMULA
|
G.f. : (1-2x+2x^2-x^3)/(1-3x+4x^2-2x^3+x^4); a(n)=3a(n-1)-4a(n-2)+2a(n-3)-a(n-4); (1/2+sqrt(5)/2)^n((1/2+sqrt(5)/10)cos(pi*n/5)+sqrt(1/10-sqrt(5)/50)sin(pi*n/5))- (sqrt(5)/2-1/2)^n((sqrt(5)/10-1/2)cos(2*pi*n/5)+sqrt(1/10+sqrt(5)/50)sin(2*pi*n/5))
a(5n)=-F(-5n-1), a(5n+1)=a(5n+2)=-F(-5n-2), a(5n+3)=0, a(5n+4)=F(-5n-4). - Michael Somos Apr 9 2005
|
|
PROGRAM
|
(PARI) a(n)=local(m); m=n%5+1; [1, -1, -1, 0, 1][m]*fibonacci(-n-(m<3)) /* Michael Somos Apr 9 2005 */
|
|
CROSSREFS
|
Cf. A000045.
Sequence in context: A032142 A032046 A131213 this_sequence A038188 A043361 A023734
Adjacent sequences: A105368 A105369 A105370 this_sequence A105372 A105373 A105374
|
|
KEYWORD
|
easy,sign
|
|
AUTHOR
|
Paul Barry (pbarry(AT)wit.ie), Apr 01 2005
|
|
|
Search completed in 0.002 seconds
|
