OFFSET
0,1
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (0, 3, 0, 1, 0, 1).
FORMULA
a(n) = 3*a(n-2) + a(n-4) + a(n-6), a(0)=3, a(1)=1, a(2)=3, a(3)=2, a(4)=11, a(5)=7.
O.g.f.: (3 + x - 6*x^2 - x^3 - x^4)/(1 - 3*x^2 - x^4 - x^6).
a(n) = T(n) + (1+(-1)^n)*(T(n-1) + (3/2)*T(n-2)).
MATHEMATICA
CoefficientList[Series[(3+x-6x^2-x^3-x^4)/(1-3x^2-x^4-x^6), {x, 0, 40}], x]
LinearRecurrence[{0, 3, 0, 1, 0, 1}, {3, 1, 3, 2, 11, 7}, 40] (* Harvey P. Dale, May 01 2014 *)
PROG
(PARI) my(x='x+O('x^40)); Vec((3+x-6*x^2-x^3-x^4)/(1-3*x^2-x^4-x^6)) \\ G. C. Greubel, Apr 21 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (3+x- 6*x^2-x^3-x^4)/(1-3*x^2-x^4-x^6) )); // G. C. Greubel, Apr 21 2019
(Sage) ((3+x-6*x^2-x^3-x^4)/(1-3*x^2-x^4-x^6)).series(x, 40).coefficients(x, sparse=False) # G. C. Greubel, Apr 21 2019
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Mario Catalani (mario.catalani(AT)unito.it), Sep 24 2002
STATUS
approved