|
| |
|
|
A099456
|
|
Expansion of 1/(1-4*x+5*x^2).
|
|
5
| |
|
|
1, 4, 11, 24, 41, 44, -29, -336, -1199, -3116, -6469, -10296, -8839, 16124, 108691, 354144, 873121, 1721764, 2521451, 1476984, -6699319, -34182196, -103232189, -242017776, -451910159, -597551756, -130656229, 2465133864
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,2
|
|
|
COMMENTS
| Associated to the knot 9_44 by the modified Chebyshev transform A(x)-> (1/(1+x^2)^2)A(x/(1+x^2)). See A099457 and A099458.
Imaginary part of (2+i)^n. [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Apr 05 2008; Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Jan 06 2009]
|
|
|
LINKS
| Dror Bar-Natan, The Rolfsen Knot Table
|
|
|
FORMULA
| a(n)=sum{k=0..floor(n/2), binomial(n-k, k)*(-5)^k*4^(n-2k)}.
E.g.f. (with offset 1): exp(x)^2*sin(x) . [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 06 2009] [Corrected by Joerg Arndt, Apr 24 2011]
a(n) = 4*a(n-1) -5*a(n-2), a(0)=1, a(1)=4. - Vincenzo Librandi, Mar 22 2011
a(n) - a(n-4) = 40 * A118444(n); a(n) - a(n-2) = 10 * A139011(n). - Paul Curtz, Apr 24 2011
|
|
|
MAPLE
| restart: G(x):=exp(x)^2*sin(x): f[0]:=G(x): for n from 1 to 54 do f[n]:=diff(f[n-1], x) od: x:=0: seq(f[n], n=1..28 ); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 06 2009]
|
|
|
MATHEMATICA
| Join[{a=1, b=4}, Table[c=4*b-5*a; a=b; b=c, {n, 100}]] (*From Vladimir Joseph Stephan Orlovsky, Jan 17 2011*)
|
|
|
PROG
| (Sage) [lucas_number1(n, 4, 5) for n in xrange(1, 29)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 22 2009]
|
|
|
CROSSREFS
| Cf. A139011. [From Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Jan 06 2009]
Sequence in context: A008070 A008096 A008209 * A008069 A047950 A008259
Adjacent sequences: A099453 A099454 A099455 * A099457 A099458 A099459
|
|
|
KEYWORD
| easy,sign
|
|
|
AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Oct 16 2004
|
| |
|
|
