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A142474
1 followed by A141015.
2
1, 0, 1, 2, 4, 9, 19, 41, 88, 189, 406, 872, 1873, 4023, 8641, 18560, 39865, 85626, 183916, 395033, 848491, 1822473, 3914488, 8407925, 18059374, 38789712, 83316385, 178955183, 384377665, 825604416, 1773314929, 3808901426, 8181135700, 17572253481, 37743426307
OFFSET
1,4
COMMENTS
Essentially the same as A078039, A141015, and A141683.
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