A142474 1 followed by A141015.

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.

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

Cf. A078039, A141015, A141683.

Sequence in context: A299106 A141015 A141683 * A078039 A305380 A275862

Adjacent sequences: A142471 A142472 A142473 * A142475 A142476 A142477

Keyword

nonn,less,easy

Author

Roger L. Bagula, Sep 21 2008

Extensions

More terms from G. C. Greubel, Jun 26 2017

Status

approved