OFFSET
1,4
LINKS
Colin Barker, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (1,2,1).
FORMULA
From Colin Barker, Jun 29 2017: (Start)
G.f.: x*(1 - x - x^2) / (1 - x - 2*x^2 - x^3).
a(n) = a(n-1) + 2*a(n-2) + a(n-3) for n>3.
(End)
MAPLE
m:=50; S:=series( x*(1-x-x^2)/(1-x-2*x^2-x^3), x, m+1):
seq(coeff(S, x, j), j=1..m); # G. C. Greubel, Apr 14 2021
MATHEMATICA
m:= 80; Table[SeriesCoefficient[Series[(1+t)/(1+t+t^3), {t, 0, m}], n], {n, 0, m, 2}]
PROG
(PARI) Vec(x*(1-x-x^2)/(1-x-2*x^2-x^3) + O(x^50)) \\ Colin Barker, Jun 29 2017
(Magma) [n le 3 select (1-(-1)^n)/2 else Self(n-1) +2*Self(n-2) +Self(n-3): n in [1..50]]; // G. C. Greubel, Apr 14 2021
(Sage)
def A142474_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( x*(1-x-x^2)/(1-x-2*x^2-x^3) ).list()
a=A142474_list(51); a[1:] # G. C. Greubel, Apr 14 2021
CROSSREFS
KEYWORD
nonn,less,easy
AUTHOR
Roger L. Bagula, Sep 21 2008
EXTENSIONS
More terms from G. C. Greubel, Jun 26 2017
STATUS
approved