A233831 a(n) = -2*a(n-1) -2*a(n-2) + a(n-3). a(0) = -1, a(1) = 1, a(2) = 1.

-1, 1, 1, -5, 9, -7, -9, 41, -71, 51, 81, -335, 559, -367, -719, 2731, -4391, 2601, 6311, -22215, 34409, -18077, -54879, 180321, -268961, 122401, 473441, -1460645, 2096809, -798887, -4056489, 11807561, -16301031, 4930451, 34548721, -95259375, 126351759

Offset: 0

Author

Michael Somos, Dec 16 2013

Keywords

• sign

Examples

			G.f. = -1 + x + x^2 - 5*x^3 + 9*x^4 - 7*x^5 - 9*x^6 + 41*x^7 - 71*x^8 + ...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (-2, -2, 1).

Crossrefs

Cf. A078004, A078054, A233828.

Programs

Magma

m:=50; R:=PowerSeriesRing(Integers(), m); Coefficients(R!((-1-x+x^2)/(1+2*x+2*x^2-x^3))); // G. C. Greubel, Aug 07 2018

Mathematica

CoefficientList[Series[(-1-x+x^2)/(1+2*x+2*x^2-x^3), {x, 0, 50}], x] (* G. C. Greubel, Aug 07 2018 *)
LinearRecurrence[{-2,-2,1},{-1,1,1},40] (* Harvey P. Dale, Nov 28 2024 *)

PARI

{a(n) = if( n<0, polcoeff( (-1 +3*x + x^2) / (1 - 2*x - 2*x^2 - x^3) + x * O(x^-n), -n), polcoeff( (-1 - x + x^2) / (1 + 2*x + 2*x^2 - x^3) + x * O(x^n), n))}

Formula

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

a(-n) = A233828(n).

a(n) - a(n-1) = -2 * (-1)^n * A078004(n).

a(n)^2 - a(n-1) * a(n+1) = -2 * (-1)^n * A078054(n-1).