A027054 a(n) = T(n, n+3), T given by A027052.

1, 8, 23, 52, 107, 210, 401, 754, 1405, 2604, 4811, 8872, 16343, 30086, 55365, 101862, 187385, 344688, 634015, 1166172, 2144963, 3945242, 7256473, 13346778, 24548597, 45151956, 83047443, 152748112, 280947631, 516743310

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:=[1,8,23,52,107];; for n in [6..33] do a[n]:=3*a[n-1]-2*a[n-2] -a[n-4]+a[n-5]; od; a; # G. C. Greubel, Nov 05 2019

Magma

R:=PowerSeriesRing(Integers(), 33); Coefficients(R!( x^3*(1+5*x+x^2-x^3-2*x^4)/((1-x)^2*(1-x-x^2-x^3)) )); // G. C. Greubel, Nov 05 2019

Maple

seq(coeff(series(x^3*(1+5*x+x^2-x^3-2*x^4)/((1-x)^2*(1-x-x^2-x^3)), x, n+1), x, n), n = 3..33); # G. C. Greubel, Nov 05 2019

Mathematica

LinearRecurrence[{3,-2,0,-1,1}, {1,8,23,52,107}, 30] (* G. C. Greubel, Nov 05 2019 *)

PARI

my(x='x+O('x^33)); Vec( x^3*(1+5*x+x^2-x^3-2*x^4)/((1-x)^2*(1-x-x^2-x^3)) ) \\ G. C. Greubel, Nov 05 2019

Sage

def A027053_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( x^3*(1+5*x+x^2-x^3-2*x^4)/((1-x)^2*(1-x-x^2-x^3)) ).list()
a=A027053_list(33); a[3:] # G. C. Greubel, Nov 05 2019

Formula

From Colin Barker, Feb 19 2016: (Start)

a(n) = 3*a(n-1) - 2*a(n-2) - a(n-4) + a(n-5) for n>6.

G.f.: x^3*(1+5*x+x^2-x^3-2*x^4)/((1-x)^2*(1-x-x^2-x^3)). (End)

a(n) = A001590(n+4) -2*n -4, n>=3. - R. J. Mathar, Jun 15 2020