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Search: id:A099456
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| A099456 |
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Expansion of 1/(1-4x+5x^2). |
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+0
5
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| 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; listen)
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OFFSET
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0,2
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COMMENT
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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]
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LINKS
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Dror Bar-Natan, The Rolfsen Knot Table
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FORMULA
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a(n)=sum{k=0..floor(n/2), binomial(n-k, k)(-5)^k*4^(n-2k)}.
G.f.: exp(x)^2*sin(x) . [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 06 2009]
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MAPLE
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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]
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PROGRAM
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(Other) sage: [lucas_number1(n, 4, 5) for n in xrange(1, 29)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 22 2009]
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CROSSREFS
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Cf. A139011. [From Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Jan 06 2009]
Sequence in context: A008070 A008096 A008209 this_sequence A008069 A047950 A008259
Adjacent sequences: A099453 A099454 A099455 this_sequence A099457 A099458 A099459
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KEYWORD
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easy,sign
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Oct 16 2004
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