A204291 G.f.: Sum_{n>=1} moebius(n)*x^n/(1 - Lucas(n)*x^n + (-1)^n*x^(2*n)), where Lucas(n) = A000204(n).

1, 0, 1, 0, 4, -3, 12, 0, 17, -10, 88, -54, 232, -28, 184, 0, 1596, -969, 4180, -1230, 4632, -198, 28656, -17388, 60020, -520, 98209, -23604, 514228, -461932, 1346268, 0, 1722688, -3570, 6672168, -5598882, 24157816, -9348, 31351552, -18606210, 165580140

Offset

1,5

Comments

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

Links

Paul D. Hanna, Table of n, a(n) for n = 1..1024

Formula

a(k) = 0 iff k = 2^n for n>=1.

Example

G.f.: A(x) = x + x^3 + 4*x^5 - 3*x^6 + 12*x^7 + 17*x^9 - 10*x^10 + 88*x^11 +...
where A(x) = x/(1-x-x^2) - x^2/(1-3*x^2+x^4) - x^3/(1-4*x^3-x^6) - x^5/(1-11*x^5-x^10) + x^6/(1-18*x^6+x^12) +...+ moebius(n)*x^n/(1 - Lucas(n)*x^n + (-1)^n*x^(2*n)) +...

Prog

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

Crossrefs

Cf. A203847, A000204 (Lucas).

Sequence in context: A270736 A270171 A270987 * A270324 A271888 A271098

Adjacent sequences: A204288 A204289 A204290 * A204292 A204293 A204294

Keyword

sign

Author

Paul D. Hanna, Jan 14 2012

Status

approved