A027024 a(n) = T(n,n+2), T given by A027023.

1, 5, 13, 27, 53, 101, 189, 351, 649, 1197, 2205, 4059, 7469, 13741, 25277, 46495, 85521, 157301, 289325, 532155, 978789, 1800277, 3311229, 6090303, 11201817, 20603357, 37895485, 69700667, 128199517, 235795677, 433695869

Offset

2,2

Links

G. C. Greubel, Table of n, a(n) for n = 2..1001

Index entries for linear recurrences with constant coefficients, signature (2,0,0,-1).

Formula

G.f.: x^2*(1+x)^3/((1-x)*(1-x-x^2-x^3)).

a(n) = a(n-1) + a(n-2) + a(n-3) + 8, for n>4. - Greg Dresden, Feb 09 2020

a(n) = A000213(n+2)-4. - R. J. Mathar, Jun 24 2020

Maple

seq(coeff(series(x^2*(1+x)^3/((1-x)*(1-x-x^2-x^3)), x, n+1), x, n), n = 2..35); # G. C. Greubel, Nov 04 2019

Mathematica

Drop[CoefficientList[Series[x^2*(1+x)^3/((1-x)*(1-x-x^2-x^3)), {x, 0, 35}], x], 2] (* or *) LinearRecurrence[{2, 0, 0, -1}, {1, 5, 13, 27}, 35] (* G. C. Greubel, Nov 04 2019 *)

Prog

(PARI) my(x='x+O('x^35)); Vec(x^2*(1+x)^3/((1-x)*(1-x-x^2-x^3))) \\ G. C. Greubel, Nov 04 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 35); Coefficients(R!( x^2*(1+x)^3/((1-x)*(1-x-x^2-x^3)) )); // G. C. Greubel, Nov 04 2019
(Sage)
def A027024_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( x^2*(1+x)^3/((1-x)*(1-x-x^2-x^3)) ).list()
a=A027024_list(35); a[2:] # G. C. Greubel, Nov 04 2019
(GAP) a:=[1, 5, 13, 27];; for n in [5..35] do a[n]:=2*a[n-1]-a[n-4]; od; a; # G. C. Greubel, Nov 04 2019

Crossrefs

Pairwise sums of A027053.

Sequence in context: A023541 A079989 A062480 * A296775 A272045 A248860

Adjacent sequences: A027021 A027022 A027023 * A027025 A027026 A027027

Keyword

nonn,easy

Author

Clark Kimberling

Status

approved