A218137 - OEIS

%I #6 Oct 21 2012 14:43:15

%S 1,1,2,3,3,6,9,11,16,27,37,40,77,117,144,207,351,482,523,999,1522,

%T 1879,2681,4560,6279,6839,12960,19799,24517,34722,59239,81793,89424,

%U 168123,257547,319880,449667,769547,1065430,1169193,2180881,3350074,4173363,5823117,9996480

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

%H Paul D. Hanna, <a href="/A218137/b218137.txt">Table of n, a(n) for n = 0..1000</a>

%e G.f.: A(x) = 1 + x + 2*x^2 + 3*x^3 + 3*x^4 + 6*x^5 + 9*x^6 + 11*x^7 + 16*x^8 +...

%e The terms equal the sum of absolute values of real and imaginary parts of the coefficients in the expansion:

%e 1/(1-x-I*x^2) = 1 + x + (1 + I)*x^2 + (1 + 2*I)*x^3 + 3*I*x^4 + (-2 + 4*I)*x^5 + (-5 + 4*I)*x^6 + (-9 + 2*I)*x^7 + (-13 - 3*I)*x^8 + (-15 - 12*I)*x^9 + (-12 - 25*I)*x^10 - 40*I*x^11 + (25 - 52*I)*x^12 + (65 - 52*I)*x^13 + (117 - 27*I)*x^14 + (169 + 38*I)*x^15 + (196 + 155*I)*x^16 + (158 + 324*I)*x^17 + (3 + 520*I)*x^18 + (-321 + 678*I)*x^19 + (-841 + 681*I)*x^20 +...

%e so that

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

%o (PARI) {a(n)=local(Cn=polcoeff(1/(1-x-I*x^2+x*O(x^n)),n));abs(real(Cn)) + abs(imag(Cn))}

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

%Y Cf. A105309, A218138.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Oct 21 2012