|
%I #9 Jan 08 2019 05:18:18
%S -1,-1,2,3,-4,-10,5,29,2,-76,-45,178,212,-361,-750,565,2282,-306,
%T -6206,-2428,15176,14353,-32719,-55104,57933,176234,-61524,-499047,
%U -97429,1271400,921652,-2887641,-3948938,5590078,13380187,-7828378,-39536779,108416,104810904
%N Expansion of -1/(1 - x + 3*x^2 - 2*x^3 + x^4 - 2*x^5 + x^6).
%H The Knot Atlas, <a href="http://katlas.math.toronto.edu/wiki/L6a1">L6a1</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (1,-3,2,-1,2,-1).
%F G.f.: 1/(x^(9/2)*f(x)), where f(x) = -x^(3/2) + 2*x^(1/2) - 1/x^(1/2) + 2/x^(3/2) - 3/x^(5/2) + 1/x^(7/2) - 1/x^(9/2) is the Jones Polynomial for the link with Dowker-Thistlethwaite notation L6a1.
%F a(n) = a(n-1) - 3*a(n-2) + 2*a(n-3) - a(n-4) + 2*a(n-5) - a(n-6), n >= 6. - _Franck Maminirina Ramaharo_, Jan 08 2019
%t CoefficientList[Series[-1/(1 - x + 3*x^2 - 2*x^3 + x^4 - 2*x^5 + x^6), {x, 0, 50}], x]
%Y Cf. A008620, A010892, A014019, A099443, A099479, A099480, A125629, A112712, A129704, A129903.
%K sign,easy
%O 0,3
%A _Roger L. Bagula_, Jun 05 2007
%E Edited by _Franck Maminirina Ramaharo_, Jan 08 2019
|
