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

3,2

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).

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

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 *)

Prog

(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
(Magma) R<x>:=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
(Sage)
def A077952_list(prec):
    P.<x> = 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
(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

Crossrefs

Sequence in context: A063036 A163673 A212132 * A366135 A120354 A206527

Adjacent sequences: A027022 A027023 A027024 * A027026 A027027 A027028

Keyword

nonn,easy

Author

Clark Kimberling

Status

approved