A233581 a(n) = 2*a(n-1) - 3*a(n-2) + a(n-3), a(0) = 1, a(1) = 0, a(2) = -1.

1, 0, -1, -1, 1, 4, 4, -3, -14, -15, 9, 49, 56, -26, -171, -208, 71, 595, 769, -176, -2064, -2831, 354, 7137, 10381, -295, -24596, -37926, -2359, 84464, 138079, 20407, -288959, -501060, -114836, 984549, 1812546, 556609, -3339871, -6537023, -2497824, 11275550

Offset

0,6

Links

G. C. Greubel, Table of n, a(n) for n = 0..2500

Index entries for linear recurrences with constant coefficients, signature (2,-3,1).

Formula

G.f.: (1 - 2*x + 2*x^2) / (1 - 2*x + 3*x^2 - x^3).

a(n) = A052921(-n). a(n)^2 - a(n-1)*a(n+1) = A034943(n).

a(n) = A127896(n) -2*A127896(n-1) + 2*A127896(n-2). - R. J. Mathar, Sep 24 2021

Example

G.f. = 1 - x^2 - x^3 + x^4 + 4*x^5 + 4*x^6 - 3*x^7 - 14*x^8 - 15*x^9 + ...

Mathematica

CoefficientList[Series[(1-2*x+2*x^2)/(1-2*x+3*x^2-x^3), {x, 0, 50}], x] (* or *) LinearRecurrence[{2, -3, 1}, {1, 0, -1}, 50] (* G. C. Greubel, Aug 08 2018 *)

Prog

(PARI) {a(n) = if( n<0, polcoeff( (1 - x) / (1 - 3*x + 2*x^2 - x^3) + x * O(x^-n), -n), polcoeff( (1 - 2*x + 2*x^2) / (1 - 2*x + 3*x^2 - x^3) + x * O(x^n), n))}
(Magma) m:=50; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((1-2*x+2*x^2)/(1-2*x+3*x^2-x^3))); // G. C. Greubel, Aug 08 2018

Crossrefs

Cf. A034943, A052921.

Sequence in context: A023530 A337365 A345294 * A193628 A306506 A241056

Adjacent sequences: A233578 A233579 A233580 * A233582 A233583 A233584

Keyword

sign

Author

Michael Somos, Dec 14 2013

Status

approved