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A218138 Sum of absolute values of real and imaginary parts of the coefficients in the expansion of 1 / (1 - x - 2*I*x^2), where I^2=-1.

%I A218138 #5 Oct 21 2012 14:51:11
%S A218138 1,1,3,5,9,19,25,59,109,147,359,653,899,2205,3915,5715,13545,23347,
%T A218138 36229,82923,138781,228653,506215,822381,1437267,3082029,4856667,
%U A218138 9000947,18714281,28578195,56172277,113328667,167517773,349394765,684430311,977894349,2166392995
%N A218138 Sum of absolute values of real and imaginary parts of the coefficients in the expansion of 1 / (1 - x - 2*I*x^2), where I^2=-1.
%H A218138 Paul D. Hanna, <a href="/A218138/b218138.txt">Table of n, a(n) for n = 0..1000</a>
%e A218138 G.f.: A(x) = 1 + x + 3*x^2 + 5*x^3 + 9*x^4 + 19*x^5 + 25*x^6 + 59*x^7 +...
%e A218138 The terms equal the norm of the complex coefficients in the expansion:
%e A218138 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 + (-3 - 144*I)*x^9 + (129 - 230*I)*x^10 + (417 - 236*I)*x^11 + (877 + 22*I)*x^12 +...
%e A218138 so that
%e A218138 a(1) = 1, a(2) = 1 + 2, a(3) = 1 + 4, a(4) = 3 + 6, a(5) = 11 + 8, ...
%o A218138 (PARI) {a(n)=local(Cn=polcoeff(1/(1-x-2*I*x^2+x*O(x^n)),n));abs(real(Cn)) + abs(imag(Cn))}
%o A218138 for(n=0,40,print1(a(n),", "))
%Y A218138 Cf. A218134, A218137.
%K A218138 nonn
%O A218138 0,3
%A A218138 _Paul D. Hanna_, Oct 21 2012