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A027026 a(n) = T(n,n+4), T given by A027023. 4
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 (list; graph; refs; listen; history; text; internal format)
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: A166080 A081272 A318293 * A251195 A087240 A044212

Adjacent sequences:  A027023 A027024 A027025 * A027027 A027028 A027029

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling

STATUS

approved

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Last modified November 30 18:37 EST 2021. Contains 349424 sequences. (Running on oeis4.)