cp's OEIS Frontend

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.

%I A204385 #7 Mar 30 2012 18:37:34
%S A204385 1,1,4,6,28,22,168,204,788,1108,5740,4356,33460,39914,149296,235416,
%T A204385 1136688,862466,6625108,7452408,30662688,46594942,225058680,170763912,
%U A204385 1266505772,1583313340,6116296036,9119790204,44560482148,30146578648,259717522848,313506783024
%N 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.
%C A204385 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)).
%H A204385 Paul D. Hanna, <a href="/A204385/b204385.txt">Table of n, a(n) for n = 1..256</a>
%F A204385 a(2^n) = A001109(2^(n-1)) for n>=1, where the g.f. of A001109 is x/(1-6*x+x^2).
%e A204385 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 +...
%e A204385 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)) +...
%o A204385 (PARI) {Pell(n)=polcoeff(x/(1-2*x-x^2+x*O(x^n)), n)}
%o A204385 {A002203(n)=polcoeff(2*(1-x)/(1-2*x-x^2+x*O(x^n)), n)}
%o A204385 {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)}
%Y A204385 Cf. A001109, A204291, A204270.
%K A204385 nonn
%O A204385 1,3
%A A204385 _Paul D. Hanna_, Jan 14 2012