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%I #22 Jan 01 2024 11:06:24
%S 1,5,18,55,149,360,757,1265,1026,-3725,-25807,-102960,-334151,-950035,
%T -2411118,-5405345,-10148899,-12907080,6506893,122884025,568871874,
%U 1984171195,5938752857,15804565920,37451559601,76625836565,120968265618,68460472135,-504475498651
%N Expansion of 1/(1 - 5x + 7x^2).
%C 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.
%H Dror Bar-Natan, <a href="http://katlas.org/wiki/Main_Page">The Rolfsen Knot Table</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (5,-7).
%F a(n) = sum{k=0..floor(n/2), binomial(n-k, k)(-7)^k*5^(n-2k)}.
%F a(n) = 5*a(n-1) - 7*a(n-2), a(0)=1, a(1)=5. - _Philippe Deléham_, Nov 15 2008
%t CoefficientList[Series[1/(1-5x+7x^2),{x,0,40}],x] (* or *) LinearRecurrence[ {5,-7},{1,5},40] (* _Harvey P. Dale_, Oct 21 2016 *)
%o (Sage) [lucas_number1(n,5,7) for n in range(1, 30)] # _Zerinvary Lajos_, Apr 22 2009
%K easy,sign
%O 0,2
%A _Paul Barry_, Oct 16 2004