A233828 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, 3, 9, 25, 71, 201, 569, 1611, 4561, 12913, 36559, 103505, 293041, 829651, 2348889, 6650121, 18827671, 53304473, 150914409, 427265435, 1209664161, 3424773601, 9696140959, 27451493281, 77720042081, 220039211683, 622970000809, 1763738467065

Offset

0,4

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).

Formula

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

a(n+2) = A101168(n). a(-n) = A233831(n).

a(n) - a(n-1) = -2 * (-1)^n * A078054(n-3).

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

Example

G.f. = -1 + x + x^2 + 3*x^3 + 9*x^4 + 25*x^5 + 71*x^6 + 201*x^7 + 569*x^8 + ...

Mathematica

CoefficientList[Series[(-1+3*x+x^2)/(1-2*x-2*x^2-x^3), {x, 0, 50}], x] (* G. C. Greubel, Aug 07 2018 *)

Prog

(PARI) {a(n) = if( n<0, polcoeff( (-1 -x + x^2) / (1 + 2*x + 2*x^2 - x^3) + x * O(x^-n), -n), polcoeff( (-1 + 3*x + x^2) / (1 - 2*x - 2*x^2 - x^3) + x * O(x^n), n))}
(Magma) m:=50; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((-1+3*x+x^2)/(1-2*x-2*x^2-x^3))); // G. C. Greubel, Aug 07 2018

Crossrefs

Cf. A078004, A078054, A101168, A233831.

Sequence in context: A046661 A309105 A101197 * A101168 A211287 A211290

Adjacent sequences: A233825 A233826 A233827 * A233829 A233830 A233831

Keyword

sign

Author

Michael Somos, Dec 16 2013

Status

approved