A073496 Expansion of (3 + 2*x + 3*x^2)/(1 + x + 3*x^2 - x^3).

3, -1, -5, 11, 3, -41, 43, 83, -253, 47, 795, -1189, -1149, 5511, -3253, -14429, 29699, 10335, -113861, 112555, 239363, -690889, 85355, 2226675, -3173629, -3421041, 15168603, -8079109, -40847741, 80253671, 34210443, -315819197, 293441539, 688226495, -1884370309, 113132363, 6228205059

Offset: 0

Author

Mario Catalani (mario.catalani(AT)unito.it), Aug 03 2002

Keywords

• sign
• easy

Comments

Old name was "a(2n), where a(n) is A073145".

Links

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

Crossrefs

Bisection of A073145.

Programs

Mathematica

CoefficientList[Series[(3 + 2*x + 3*x^2)/(1 + x + 3*x^2 - x^3), {x, 0, 50}], x]
LinearRecurrence[{-1,-3,1},{3,-1,-5},40] (* Harvey P. Dale, Aug 22 2018 *)

Formula

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

a(2n)=-a(2n-2)-3a(2n-4)+a(2n-6), a(0)=3, a(2)=-1, a(4)=-5.

Recurrence: a(n) = a(n-3) - 3a(n-2) - a(n-1), starting 3,-1,-5.