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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
OFFSET
2,2
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
a(n) = A000213(n+2)-4. - R. J. Mathar, Jun 24 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
KEYWORD
nonn,easy
STATUS
approved