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A074475 a(n) = Sum_{j=0..floor(n/2)} T(2*j + q), where T(n) are generalized tribonacci numbers (A001644) and q = n - 2*floor(n/2). 2

%I

%S 3,1,6,8,17,29,56,100,187,341,630,1156,2129,3913,7200,13240,24355,

%T 44793,82390,151536,278721,512645,942904,1734268,3189819,5866989,

%U 10791078,19847884,36505953,67144913,123498752,227149616,417793283

%N a(n) = Sum_{j=0..floor(n/2)} T(2*j + q), where T(n) are generalized tribonacci numbers (A001644) and q = n - 2*floor(n/2).

%C a(n) is the convolution of T(n) with the sequence (1,0,1,0,1,0,...).

%H G. C. Greubel, <a href="/A074475/b074475.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,2,2,1).

%F a(n) = 2*a(n-2) + 2*a(n-3) + a(n-4), a(0)=3, a(1)=1, a(2)=6, a(3)=8.

%F G.f.: (3+x)/(1-2*x^2-2*x^3-x^4).

%t CoefficientList[Series[(3+x)/(1-2*x^2-2*x^3-x^4), {x, 0, 40}], x]

%t LinearRecurrence[{0,2,2,1},{3,1,6,8},40] (* _Harvey P. Dale_, Jul 08 2017 *)

%o (PARI) my(x='x+O('x^40)); Vec((3+x)/(1-2*x^2-2*x^3-x^4)) \\ _G. C. Greubel_, Apr 21 2019

%o (MAGMA) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (3+x)/(1-2*x^2-2*x^3-x^4) )); // _G. C. Greubel_, Apr 21 2019

%o (Sage) ((3+x)/(1-2*x^2-2*x^3-x^4)).series(x, 40).coefficients(x, sparse=False) # _G. C. Greubel_, Apr 21 2019

%Y Cf. A001644, A074331.

%K easy,nonn

%O 0,1

%A Mario Catalani (mario.catalani(AT)unito.it), Aug 23 2002

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Last modified July 16 11:09 EDT 2020. Contains 335784 sequences. (Running on oeis4.)