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A074585 a(n)= Sum_{j=0..floor(n/2)} A073145(2*j + q), where q = 2*(n/2 - floor(n/2)). 1

%I

%S 3,-1,2,4,-3,3,8,-12,11,11,-30,32,13,-73,96,-8,-157,263,-110,-308,685,

%T -485,-504,1676,-1653,-525,3858,-4984,605,8239,-13824,6192,15875,

%U -35889,26210,25556,-87651,88307,24904,-200860,264267,-38501,-426622

%N a(n)= Sum_{j=0..floor(n/2)} A073145(2*j + q), where q = 2*(n/2 - floor(n/2)).

%C a(n) is the convolution of A073145(n) with the sequence (1,0,1,0,1,0, ...).

%C a(n) is also the sum of the reflected (see A074058) sequence of the generalized tribonacci sequence (A001644).

%H G. C. Greubel, <a href="/A074585/b074585.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (-1,0,2,1,-1).

%F a(n) = -a(n-1) + 2*a(n-3) + a(n-4) - a(n-5), a(0) = 3, a(1) = -1, a(2) = 2, a(3) = 4, a(4) = -3.

%F G.f.: (3 + 2*x + x^2)/(1 + x - 2*x^3 - x^4 + x^5).

%t CoefficientList[ Series[(3+2*x+x^2)/(1+x-2*x^3-x^4+x^5), {x, 0, 50}], x]

%o (PARI) my(x='x+O('x^50)); Vec((3+2*x+x^2)/(1+x-2*x^3-x^4+x^5)) \\ _G. C. Greubel_, Apr 13 2019

%o (MAGMA) R<x>:=PowerSeriesRing(Integers(), 50); Coefficients(R!( (3+2*x+x^2)/(1+x-2*x^3-x^4+x^5) )); // _G. C. Greubel_, Apr 13 2019

%o (Sage) ((3+2*x+x^2)/(1+x-2*x^3-x^4+x^5)).series(x, 50).coefficients(x, sparse=False) # _G. C. Greubel_, Apr 13 2019

%Y Cf. A073145, A074058, A001644, A074331, A074392, A074475.

%K easy,sign

%O 0,1

%A Mario Catalani (mario.catalani(AT)unito.it), Aug 28 2002

%E More terms from _Robert G. Wilson v_, Aug 29 2002

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Last modified June 3 05:29 EDT 2020. Contains 334798 sequences. (Running on oeis4.)