A027026 a(n) = T(n,n+4), T given by A027023.

1, 25, 85, 215, 477, 985, 1949, 3755, 7113, 13329, 24805, 45959, 84917, 156625, 288573, 531323, 977873, 1799273, 3310133, 6089111, 11200525, 20601961, 37893981, 69699051, 128197785, 235793825, 433693893, 797688967, 1467180389

Offset

4,2

Links

G. C. Greubel, Table of n, a(n) for n = 4..1003

Index entries for linear recurrences with constant coefficients, signature (4,-5,2,-1,2,-1).

Formula

G.f.: x^4*(1 +21*x -10*x^2 -2*x^3 -7*x^4 +5*x^5)/((1-x)^3*(1-x-x^2-x^3)). - Ralf Stephan, Feb 11 2004

a(n) = A000213(n+4) -2*n*(n+3), n>3. - R. J. Mathar, Jun 24 2020

Maple

seq(coeff(series(x^4*(1 +21*x -10*x^2 -2*x^3 -7*x^4 +5*x^5)/((1-x)^3*(1-x-x^2-x^3)), x, n+1), x, n), n = 4..40); # G. C. Greubel, Nov 04 2019

Mathematica

Drop[CoefficientList[Series[x^4*(1+21*x-10*x^2-2*x^3-7*x^4 +5*x^5)/((1-x)^3*(1-x-x^2-x^3)), {x, 0, 40}], x], 4] (* or *) LinearRecurrence[{4, -5, 2, -1, 2, -1}, {1, 25, 85, 215, 477, 985}, 40] (* G. C. Greubel, Nov 04 2019 *)

Prog

(PARI) my(x='x+O('x^40)); Vec(x^4*(1 +21*x -10*x^2 -2*x^3 -7*x^4 +5*x^5)/((1-x)^3*(1-x-x^2-x^3))) \\ G. C. Greubel, Nov 04 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( x^4*(1 +21*x -10*x^2 -2*x^3 -7*x^4 +5*x^5)/((1-x)^3*(1-x-x^2-x^3)) )); // G. C. Greubel, Nov 04 2019
(Sage)
def A027026_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P(x^4*(1 +21*x -10*x^2 -2*x^3 -7*x^4 +5*x^5)/((1-x)^3*(1-x-x^2-x^3))).list()
a=A027026_list(50); a[4:] # G. C. Greubel, Nov 04 2019
(GAP) a:=[1, 25, 85, 215, 477, 985];; for n in [7..40] do a[n]:=4*a[n-1] -5*a[n-2]+2*a[n-3]-a[n-4]+2*a[n-5]-a[n-6]; od; a; # G. C. Greubel, Nov 04 2019

Crossrefs

Sequence in context: A371016 A081272 A318293 * A251195 A087240 A044212

Adjacent sequences: A027023 A027024 A027025 * A027027 A027028 A027029

Keyword

nonn,easy

Author

Clark Kimberling

Status

approved