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A218135 Norm of coefficients in the expansion of 1 / (1 - x - 2*I*x^2), where I^2=-1.

%I A218135 #7 Oct 21 2012 14:34:16
%S A218135 1,1,5,17,45,185,533,1921,6205,20745,69541,229585,769613,2552537,
%T A218135 8515125,28340513,94357853,314301865,1046284741,3484682865,
%U A218135 11602442605,38636214649,128653931093,428398492865,1426535718525,4750159951433,15817576773605,52670623373329
%N A218135 Norm of coefficients in the expansion of 1 / (1 - x - 2*I*x^2), where I^2=-1.
%C A218135 The radius of convergence of g.f. equals (1 + sqrt(65) - sqrt(2)*sqrt(1+sqrt(65)))/16 = 0.30031050...
%F A218135 G.f.: (1-4*x^2) / (1 - x - 8*x^2 - 4*x^3 + 16*x^4).
%e A218135 G.f.: A(x) = 1 + 4*x + 17*x^2 + 80*x^3 + 369*x^4 + 1700*x^5 + 7841*x^6 +...
%e A218135 The terms equal the norm of the complex coefficients in the expansion:
%e A218135 1/(1-x-2*I*x^2) = 1 + x + (1 + 2*I)*x^2 + (1 + 4*I)*x^3 + (-3 + 6*I)*x^4 + (-11 + 8*I)*x^5 + (-23 + 2*I)*x^6 + (-39 - 20*I)*x^7 + (-43 - 66*I)*x^8 +...
%e A218135 so that
%e A218135 a(1) = 1, a(2) = 1 + 2^2, a(3) = 1 + 4^2, a(4) = 3^2 + 6^2, a(5) = 11^2 + 8^2, ...
%o A218135 (PARI) {a(n)=norm(polcoeff(1/(1-x-2*I*x^2+x*O(x^n)), n))}
%o A218135 for(n=0,30,print1(a(n),", "))
%Y A218135 Cf. A105309, A218134.
%K A218135 nonn
%O A218135 0,3
%A A218135 _Paul D. Hanna_, Oct 21 2012