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

1, 1, 5, 17, 45, 185, 533, 1921, 6205, 20745, 69541, 229585, 769613, 2552537, 8515125, 28340513, 94357853, 314301865, 1046284741, 3484682865, 11602442605, 38636214649, 128653931093, 428398492865, 1426535718525, 4750159951433, 15817576773605, 52670623373329

Offset: 0

Author

Paul D. Hanna, Oct 21 2012

Keywords

• nonn

Comments

The radius of convergence of g.f. equals (1 + sqrt(65) - sqrt(2)*sqrt(1+sqrt(65)))/16 = 0.30031050...

Examples

			G.f.: A(x) = 1 + 4*x + 17*x^2 + 80*x^3 + 369*x^4 + 1700*x^5 + 7841*x^6 +...
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 +...
so that
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, ...
		

Crossrefs

Cf. A105309, A218134.

Programs

PARI

{a(n)=norm(polcoeff(1/(1-x-2*I*x^2+x*O(x^n)), n))}
for(n=0,30,print1(a(n),", "))

Formula

G.f.: (1-4*x^2) / (1 - x - 8*x^2 - 4*x^3 + 16*x^4).