A204059 a(n) = Pell(n) * Sum_{d|n} (-1)^(n/d) / Pell(d), where Pell(n) = A000129(n).

1, -1, 6, -17, 30, -48, 170, -645, 1183, -1270, 5742, -22604, 33462, -40868, 240756, -746637, 1136690, -1884529, 6625110, -23217030, 46565244, -46627416, 225058682, -975425316, 1356970471, -1583502622, 9182205852, -26257649200, 44560482150, -77433044928

Offset

1,3

Links

Table of n, a(n) for n=1..30.

Formula

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

a(2*n-1) = A203797(2*n-1).

Example

G.f.: A(x) = x - x^2 + 6*x^3 - 17*x^4 + 30*x^5 - 48*x^6 + 170*x^7 +...
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^4/(1+34*x^4+x^8) + x^5/(1+82*x^5-x^10) + x^6/(1+198*x^6+x^12) +...+ 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)}
{a(n)=Pell(n) * sumdiv(n, d, -(-1)^(n/d)/Pell(d))}
(PARI) /* G.f. using companion Pell numbers: */
{A002203(n)=polcoeff(2*(1-x)/(1-2*x-x^2+x*O(x^n)), n)}
{a(n)=polcoeff(sum(m=1, n, x^m/(1 + A002203(m)*x^m + (-1)^m*x^(2*m) +x*O(x^n))), n)}

Crossrefs

Cf. A203797, A111075, A203802, A000129, A002203.

Sequence in context: A061875 A063230 A212461 * A067559 A096426 A130051

Adjacent sequences: A204056 A204057 A204058 * A204060 A204061 A204062

Keyword

sign

Author

Paul D. Hanna, Jan 13 2012

Status

approved