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Search: id:A099453
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| A099453 |
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Expansion of 1/(1-7x+11x^2). |
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+0
4
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| 1, 7, 38, 189, 905, 4256, 19837, 92043, 426094, 1970185, 9104261, 42057792, 194257673, 897167999, 4143341590, 19134543141, 88365044497, 408075336928, 1884511869029, 8702754376995, 40189650079646, 185597252410577
(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 8_12 by the modified Chebyshev transform A(x)-> (1/(1+x^2)^2)A(x/(1+x^2)). See A099454 and A099455.
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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)(-11)^k*7^(n-2k)}.
a(n) = ((7+sqrt(5))^n-(7-sqrt(5))^n)/(2^n*sqrt(5)), n > 0. Binomial transform of A030191 (Scaled Chebyshev U-polynomial evaluated at sqrt(5)/2); 3rd binomial transform of Fib(n). - Creighton Dement (creighton.k.dement(AT)uni-oldenburg.de), Apr 19 2005
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PROGRAM
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(Other) sage: [lucas_number1(n, 7, 11) for n in xrange(1, 23)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 23 2009]
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CROSSREFS
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Sequence in context: A034858 A114290 A000531 this_sequence A026763 A037696 A026895
Adjacent sequences: A099450 A099451 A099452 this_sequence A099454 A099455 A099456
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KEYWORD
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easy,nonn
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Oct 16 2004
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