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A099453
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Expansion of 1/(1-7x+11x^2).
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7
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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; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| 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
| Dror Bar-Natan, The Rolfsen Knot Table
Index to sequences with linear recurrences with constant coefficients, signature (7,-11)
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FORMULA
| 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
a(n) = 7*a(n-1) -11*a(n-2), n>=2. - Vincenzo Librandi, Mar 18 2011
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MATHEMATICA
| Join[{a=1, b=7}, Table[c=7*b-11*a; a=b; b=c, {n, 60}]] (*From Vladimir Joseph Stephan Orlovsky, Jan 18 2011*)
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PROG
| (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
| Sequence in context: A034858 A114290 A000531 * A026763 A037696 A026895
Adjacent sequences: A099450 A099451 A099452 * A099454 A099455 A099456
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Oct 16 2004
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