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A074475
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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).
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2
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3, 1, 6, 8, 17, 29, 56, 100, 187, 341, 630, 1156, 2129, 3913, 7200, 13240, 24355, 44793, 82390, 151536, 278721, 512645, 942904, 1734268, 3189819, 5866989, 10791078, 19847884, 36505953, 67144913, 123498752, 227149616, 417793283
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OFFSET
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0,1
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COMMENTS
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a(n) is the convolution of T(n) with the sequence (1,0,1,0,1,0,...).
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LINKS
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FORMULA
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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.
G.f.: (3+x)/(1-2*x^2-2*x^3-x^4).
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MATHEMATICA
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CoefficientList[Series[(3+x)/(1-2*x^2-2*x^3-x^4), {x, 0, 40}], x]
LinearRecurrence[{0, 2, 2, 1}, {3, 1, 6, 8}, 40] (* Harvey P. Dale, Jul 08 2017 *)
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PROG
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(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
(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
(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
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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Mario Catalani (mario.catalani(AT)unito.it), Aug 23 2002
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STATUS
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approved
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