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A141523
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Expansion of (3-2*x-3*x^2)/(1-x-x^2-x^3).
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53
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3, 1, 1, 5, 7, 13, 25, 45, 83, 153, 281, 517, 951, 1749, 3217, 5917, 10883, 20017, 36817, 67717, 124551, 229085, 421353, 774989, 1425427, 2621769, 4822185, 8869381, 16313335, 30004901, 55187617, 101505853, 186698371, 343391841
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OFFSET
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0,1
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LINKS
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FORMULA
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a(0)=3; a(1)=1; a(2)=1; thereafter a(n) = a(n-1) + a(n-2) + a(n-3).
O.g.f.: (3-2*x-3*x^2)/(1-x-x^2-x^3).
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MATHEMATICA
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a[0]=3; a[1]=1; a[2]=1; a[n_]:= a[n]=a[n-1]+a[n-2]+a[n-3]; Table[a[n], {n, 0, 40}]
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PROG
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(Magma) I:=[3, 1, 1]; [n le 3 select I[n] else Self(n-1)+Self(n-2) +Self(n-3): n in [1..40]]; // Vincenzo Librandi, Oct 17 2012
(PARI) my(x='x+O('x^40)); Vec((3-2*x-3*x^2)/(1-x-x^2-x^3)) \\ G. C. Greubel, Apr 22 2019
(Sage) ((3-2*x-3*x^2)/(1-x-x^2-x^3)).series(x, 40).coefficients(x, sparse=False) # G. C. Greubel, Apr 22 2019
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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