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A073717
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a(n) = T(2n+1), where T(n) are the tribonacci numbers A000073.
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4
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0, 1, 4, 13, 44, 149, 504, 1705, 5768, 19513, 66012, 223317, 755476, 2555757, 8646064, 29249425, 98950096, 334745777, 1132436852, 3831006429, 12960201916, 43844049029, 148323355432, 501774317241, 1697490356184, 5742568741225
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n) = 3*a(n-1) +a(n-2) +a(n-3), a(0)=0, a(1)=1, a(2)=4.
G.f.: x*(1+x)/(1-3*x-x^2-x^3).
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MATHEMATICA
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CoefficientList[Series[(x+x^2)/(1-3x-x^2-x^3), {x, 0, 30}], x]
LinearRecurrence[{3, 1, 1}, {0, 1, 4}, 30] (* Harvey P. Dale, Sep 07 2015 *)
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PROG
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(Magma) [n le 3 select (n-1)^2 else 3*Self(n-1) +Self(n-2) +Self(n-3): n in [1..31]]; // G. C. Greubel, Nov 19 2021
(Sage)
P.<x> = PowerSeriesRing(ZZ, prec)
return P( x*(1+x)/(1-3*x-x^2-x^3) ).list()
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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 05 2002
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STATUS
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approved
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