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a(n) = Sum_{k=0..n} S(k)*S(n-k), convolution of S=A001644 with itself.
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%I #11 Sep 08 2022 08:45:06

%S 9,6,19,48,89,190,391,784,1577,3142,6219,12256,24041,46974,91471,

%T 177568,343753,663814,1278979,2459152,4719417,9041470,17294039,

%U 33030320,62999145,120006214,228327099,433939904,823854793,1562602238

%N a(n) = Sum_{k=0..n} S(k)*S(n-k), convolution of S=A001644 with itself.

%H G. C. Greubel, <a href="/A073782/b073782.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2,1,0,-3,-2,-1).

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

%t CoefficientList[Series[(3-2x-x^2)^2/(1-x-x^2-x^3)^2, {x, 0, 30}], x]

%o (PARI) my(x='x+O('x^30)); Vec((3-2*x-x^2)^2/(1-x-x^2-x^3)^2) \\ _G. C. Greubel_, Apr 12 2019

%o (Magma) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (3-2*x-x^2)^2/(1-x-x^2-x^3)^2 )); // _G. C. Greubel_, Apr 12 2019

%o (Sage) ((3-2*x-x^2)^2/(1-x-x^2-x^3)^2).series(x, 30).coefficients(x, sparse=False) # _G. C. Greubel_, Apr 12 2019

%Y Cf. A001644.

%K easy,nonn

%O 0,1

%A Mario Catalani (mario.catalani(AT)unito.it), Aug 11 2002