A204385 G.f.: Sum_{n>=1} moebius(n)*x^n/(1 - A002203(n)*x^n + (-1)^n*x^(2*n)), where A002203 is the companion Pell numbers.

1, 1, 4, 6, 28, 22, 168, 204, 788, 1108, 5740, 4356, 33460, 39914, 149296, 235416, 1136688, 862466, 6625108, 7452408, 30662688, 46594942, 225058680, 170763912, 1266505772, 1583313340, 6116296036, 9119790204, 44560482148, 30146578648, 259717522848, 313506783024

Offset: 1

Author

Paul D. Hanna, Jan 14 2012

Keywords

• nonn

Comments

Compare g.f. to the identity: x = Sum_{n>=1} moebius(n)*Pell(n)*x^n/(1 - A002203(n)*x^n + (-1)^n*x^(2*n)).

Examples

			G.f.: A(x) = x + x^2 + 4*x^3 + 6*x^4 + 28*x^5 + 22*x^6 + 168*x^7 + 204*x^8 +...
where A(x) = x/(1-2*x-x^2) - x^2/(1-6*x^2+x^4) - x^3/(1-14*x^3-x^6) - x^5/(1-82*x^5-x^10) + x^6/(1-198*x^6+x^12) +...+ moebius(n)*x^n/(1 - A002203(n)*x^n + (-1)^n*x^(2*n)) +...
		

Links

• Paul D. Hanna, Table of n, a(n) for n = 1..256

Crossrefs

Cf. A001109, A204291, A204270.

Programs

PARI

{Pell(n)=polcoeff(x/(1-2*x-x^2+x*O(x^n)), n)}
{A002203(n)=polcoeff(2*(1-x)/(1-2*x-x^2+x*O(x^n)), n)}
{a(n)=polcoeff(sum(m=1,n,moebius(m)*x^m/(1-A002203(m)*x^m+(-1)^m*x^(2*m)+x*O(x^n))),n)}

Formula

a(2^n) = A001109(2^(n-1)) for n>=1, where the g.f. of A001109 is x/(1-6*x+x^2).