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Search: id:A099450
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| A099450 |
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Expansion of 1/(1-5x+7x^2). |
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+0
3
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| 1, 5, 18, 55, 149, 360, 757, 1265, 1026, -3725, -25807, -102960, -334151, -950035, -2411118, -5405345, -10148899, -12907080, 6506893, 122884025, 568871874, 1984171195, 5938752857, 15804565920, 37451559601, 76625836565, 120968265618, 68460472135, -504475498651
(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 7_7 by the modified Chebyshev transform A(x)-> (1/(1+x^2)^2)A(x/(1+x^2)). See A099451 and A099452.
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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)(-7)^k*5^(n-2k)}.
a(n)=5*a(n-1)-7*a(n-2), a(0)=1, a(1)=5. [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 15 2008]
a(n)=(1/2)*[(5/2)+(1/2)*I*sqrt(3)]^(n-1)+(1/2)*[(5/2)-(1/2)*I*sqrt(3)]^(n-1)-(5/6)*I*[(5/2)+(1/2)*I *sqrt(3)]^(n-1)*sqrt(3)+(5/6)*I*[(5/2)-(1/2)*I*sqrt(3)]^(n-1)*sqrt(3), with n>=0 and I=sqrt(-1) [From Paolo P. Lava (ppl(AT)spl.at), Nov 19 2008]
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PROGRAM
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(Other) sage: [lucas_number1(n, 5, 7) for n in xrange(1, 30)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 22 2009]
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CROSSREFS
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Sequence in context: A056782 A081492 A011845 this_sequence A145129 A001793 A093374
Adjacent sequences: A099447 A099448 A099449 this_sequence A099451 A099452 A099453
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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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