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

0,1

Comments

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

Links

Table of n, a(n) for n=0..36.

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

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.

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 *)

Crossrefs

Bisection of A073145.

Sequence in context: A219078 A266033 A105064 * A176122 A370380 A091623

Adjacent sequences: A073493 A073494 A073495 * A073497 A073498 A073499

Keyword

sign,easy

Author

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

Status

approved