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

1,3

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)).

Links

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

Formula

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

Example

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)) +...

Prog

(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)}

Crossrefs

Cf. A001109, A204291, A204270.

Sequence in context: A013078 A106286 A066293 * A341045 A050881 A229719

Adjacent sequences: A204382 A204383 A204384 * A204386 A204387 A204388

Keyword

nonn

Author

Paul D. Hanna, Jan 14 2012

Status

approved