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.

1, 1, 3, 5, 9, 19, 25, 59, 109, 147, 359, 653, 899, 2205, 3915, 5715, 13545, 23347, 36229, 82923, 138781, 228653, 506215, 822381, 1437267, 3082029, 4856667, 9000947, 18714281, 28578195, 56172277, 113328667, 167517773, 349394765, 684430311, 977894349, 2166392995

Offset

0,3

Links

Paul D. Hanna, Table of n, a(n) for n = 0..1000

Example

G.f.: A(x) = 1 + x + 3*x^2 + 5*x^3 + 9*x^4 + 19*x^5 + 25*x^6 + 59*x^7 +...
The terms equal the norm of the complex coefficients in the expansion:
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 +...
so that
a(1) = 1, a(2) = 1 + 2, a(3) = 1 + 4, a(4) = 3 + 6, a(5) = 11 + 8, ...

Prog

(PARI) {a(n)=local(Cn=polcoeff(1/(1-x-2*I*x^2+x*O(x^n)), n)); abs(real(Cn)) + abs(imag(Cn))}
for(n=0, 40, print1(a(n), ", "))

Crossrefs

Cf. A218134, A218137.

Sequence in context: A018098 A108859 A032385 * A192230 A291222 A339916

Adjacent sequences: A218135 A218136 A218137 * A218139 A218140 A218141

Keyword

nonn

Author

Paul D. Hanna, Oct 21 2012

Status

approved