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%I #24 Jun 12 2021 13:57:28
%S 1,6,23,35,134,204,781,1189,4552,6930,26531,40391,154634,235416,
%T 901273,1372105,5253004,7997214,30616751,46611179,178447502,271669860,
%U 1040068261,1583407981,6061962064,9228778026,35331704123,53789260175,205928262674
%N Expansion of (1 + 6*x + 17*x^2 - x^3 - 3*x^4)/(1 - 6*x^2 + x^4).
%C Also, values i where A067060(i)/i reaches a new maximum (conjectured).
%H E. I. Emerson, <a href="http://www.fq.math.ca/Scanned/7-3/emerson.pdf">Recurrent Sequences in the Equation DQ^2=R^2+N</a>, Fib. Quart., 7 (1969), pp. 231-242.
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,6,0,-1)
%F G.f.: (1+6*x+17*x^2-x^3-3*x^4)/((1+2*x-x^2)*(1-2*x-x^2)).
%F a(2n) = A038723(n+1), n>0.
%F a(2n+1) = A001109(n+2).
%F a(n) = (1/4) * (A135532(n+3) + (-1)^n*A001333(n+2) ).
%t CoefficientList[Series[(1+6x+17x^2-x^3-3x^4)/(1-6x^2+x^4),{x,0,40}],x] (* or *) LinearRecurrence[{0,6,0,-1},{1,6,23,35,134},40] (* _Harvey P. Dale_, Jun 12 2021 *)
%o (PARI) a(n)=polcoeff((-3*x^4-x^3+17*x^2+6*x+1)/(x^4-6*x^2+1)+O(x^100),n)
%Y Cf. A041017.
%K nonn,easy
%O 0,2
%A _Ralf Stephan_, Sep 23 2013
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