A027025 a(n) = T(n,n+3), T given by A027023.

1, 11, 33, 77, 161, 319, 613, 1157, 2161, 4011, 7417, 13685, 25217, 46431, 85453, 157229, 289249, 532075, 978705, 1800189, 3311137, 6090207, 11201717, 20603253, 37895377, 69700555, 128199401, 235795557, 433695745, 797690943

Offset: 3

Author

Clark Kimberling

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 3..1002
• Index entries for linear recurrences with constant coefficients, signature (3,-2,0,-1,1).

Programs

GAP

a:=[1,11,33,77,161];; for n in [6..30] do a[n]:=3*a[n-1]-2*a[n-2]-a[n-4] +a[n-5]; od; a; # G. C. Greubel, Nov 04 2019

Magma

R:=PowerSeriesRing(Integers(), 40); Coefficients(R!( x^3*(1+8*x+2*x^2-3*x^4)/((1-x)^2*(1-x-x^2-x^3)) )); // G. C. Greubel, Nov 04 2019

Maple

seq(coeff(series(x^4/((1+2*x)*(2*x^3+x^2-2*x+1)), x, n+1), x, n), n = 3..40); # G. C. Greubel, Nov 04 2019

Mathematica

Drop[CoefficientList[Series[x^3*(1+8*x+2*x^2-3*x^4)/((1-x)^2*(1-x-x^2-x^3)), {x,0,40}], x], 3] (* or *) LinearRecurrence[{3,-2,0,-1,1}, {1, 11,33,77,161}, 40] (* G. C. Greubel, Nov 04 2019 *)

PARI

my(x='x+O('x^40)); Vec(x^3*(1+8*x+2*x^2-3*x^4)/((1-x)^2*(1-x-x^2-x^3))) \\ G. C. Greubel, Nov 04 2019

Sage

def A077952_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P(x^3*(1+8*x+2*x^2-3*x^4)/((1-x)^2*(1-x-x^2-x^3))).list()
a=A077952_list(40); a[3:] # G. C. Greubel, Nov 04 2019

Formula

G.f.: x^3*(1+8*x+2*x^2-3*x^4)/((1-x)^2*(1-x-x^2-x^3)).

a(n) = A000213(n+3) -4*(n+1). - R. J. Mathar, Jun 24 2020