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

Author

Clark Kimberling

Keywords

• nonn
• easy

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).

Crossrefs

Pairwise sums of A027053.

Programs

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

Magma

R:=PowerSeriesRing(Integers(), 35); Coefficients(R!( x^2*(1+x)^3/((1-x)*(1-x-x^2-x^3)) )); // G. C. Greubel, Nov 04 2019

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 *)

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

Sage

def A027024_list(prec):
    P. = 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

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