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A218136 Norm of coefficients in the expansion of 1 / (1 - 3*x + 2*I*x^2), where I^2=-1.

%I A218136 #10 Mar 22 2023 08:42:33
%S A218136 1,9,85,873,8845,89505,906373,9177849,92932285,941010705,9528455221,
%T A218136 96482899305,976963204333,9892500250113,100169136977125,
%U A218136 1014289183762137,10270454347410973,103996211523970545,1053041242918825621,10662848608027795785,107969503760905131085
%N A218136 Norm of coefficients in the expansion of 1 / (1 - 3*x + 2*I*x^2), where I^2=-1.
%C A218136 The radius of convergence of g.f. equals (9+sqrt(145) - 3*sqrt(2)*sqrt(9+sqrt(145)))/16 = 0.0987579662...
%H A218136 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (9, 8, 36, -16).
%F A218136 G.f.: (1-4*x^2) / (1 - 9*x - 8*x^2 - 36*x^3 + 16*x^4).
%e A218136 G.f.: A(x) = 1 + 9*x + 85*x^2 + 873*x^3 + 8845*x^4 + 89505*x^5 + 906373*x^6 +...
%e A218136 The terms equal the norm of the complex coefficients in the expansion:
%e A218136 1/(1-3*x+2*I*x^2) = 1 + 3*x + (9 - 2*I)*x^2 + (27 - 12*I)*x^3 + (77 - 54*I)*x^4 + (207 - 216*I)*x^5 + (513 - 802*I)*x^6 + (1107 - 2820*I)*x^7 +...
%e A218136 so that
%e A218136 a(1) = 3^2, a(2) = 9^2 + 2^2, a(3) = 27^2 + 12^2, a(4) = 77^2 + 54^2, a(5) = 207^2 + 216^2, ...
%t A218136 CoefficientList[Series[(1-4x^2)/(1-9x-8x^2-36x^3+16x^4),{x,0,20}],x] (* or *) LinearRecurrence[{9,8,36,-16},{1,9,85,873},30] (* _Harvey P. Dale_, Mar 22 2023 *)
%o A218136 (PARI) {a(n)=norm(polcoeff(1/(1-3*x+2*I*x^2+x*O(x^n)), n))}
%o A218136 for(n=0,30,print1(a(n),", "))
%Y A218136 Cf. A105309, A218134, A218135.
%K A218136 nonn
%O A218136 0,2
%A A218136 _Paul D. Hanna_, Oct 21 2012