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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, 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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 21 15:27 EDT 2021. Contains 347598 sequences. (Running on oeis4.)