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A027024 a(n) = T(n,n+2), T given by A027023. 4
1, 5, 13, 27, 53, 101, 189, 351, 649, 1197, 2205, 4059, 7469, 13741, 25277, 46495, 85521, 157301, 289325, 532155, 978789, 1800277, 3311229, 6090303, 11201817, 20603357, 37895485, 69700667, 128199517, 235795677, 433695869 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,2

LINKS

G. C. Greubel, Table of n, a(n) for n = 2..1001

Index entries for linear recurrences with constant coefficients, signature (2,0,0,-1).

FORMULA

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

a(n) = a(n-1) + a(n-2) + a(n-3) + 8, for n>4. - Greg Dresden, Feb 09 2020

MAPLE

seq(coeff(series(x^2*(1+x)^3/((1-x)*(1-x-x^2-x^3)), x, n+1), x, n), n = 2..35); # G. C. Greubel, Nov 04 2019

MATHEMATICA

Drop[CoefficientList[Series[x^2*(1+x)^3/((1-x)*(1-x-x^2-x^3)), {x, 0, 35}], x], 2] (* or *) LinearRecurrence[{2, 0, 0, -1}, {1, 5, 13, 27}, 35] (* G. C. Greubel, Nov 04 2019 *)

PROG

(PARI) my(x='x+O('x^35)); Vec(x^2*(1+x)^3/((1-x)*(1-x-x^2-x^3))) \\ G. C. Greubel, Nov 04 2019

(MAGMA) R<x>:=PowerSeriesRing(Integers(), 35); Coefficients(R!( x^2*(1+x)^3/((1-x)*(1-x-x^2-x^3)) )); // G. C. Greubel, Nov 04 2019

(Sage)

def A027024_list(prec):

    P.<x> = PowerSeriesRing(ZZ, prec)

    return P( x^2*(1+x)^3/((1-x)*(1-x-x^2-x^3)) ).list()

a=A027024_list(35); a[2:] # G. C. Greubel, Nov 04 2019

(GAP) a:=[1, 5, 13, 27];; for n in [5..35] do a[n]:=2*a[n-1]-a[n-4]; od; a; # G. C. Greubel, Nov 04 2019

CROSSREFS

Pairwise sums of A027053.

Sequence in context: A023541 A079989 A062480 * A296775 A272045 A248860

Adjacent sequences:  A027021 A027022 A027023 * A027025 A027026 A027027

KEYWORD

nonn,changed

AUTHOR

Clark Kimberling

STATUS

approved

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Last modified February 17 17:59 EST 2020. Contains 331999 sequences. (Running on oeis4.)