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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.
2

%I #5 Oct 21 2012 14:51:11

%S 1,1,3,5,9,19,25,59,109,147,359,653,899,2205,3915,5715,13545,23347,

%T 36229,82923,138781,228653,506215,822381,1437267,3082029,4856667,

%U 9000947,18714281,28578195,56172277,113328667,167517773,349394765,684430311,977894349,2166392995

%N 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 Paul D. Hanna, <a href="/A218138/b218138.txt">Table of n, a(n) for n = 0..1000</a>

%e 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 The terms equal the norm of the complex coefficients in the expansion:

%e 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 so that

%e a(1) = 1, a(2) = 1 + 2, a(3) = 1 + 4, a(4) = 3 + 6, a(5) = 11 + 8, ...

%o (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 for(n=0,40,print1(a(n),", "))

%Y Cf. A218134, A218137.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Oct 21 2012