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A113032
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a(n) = Sum_{k=0..floor(n/8)} binomial(n-5*k, 3*k).
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1
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1, 1, 1, 1, 1, 1, 1, 1, 2, 5, 11, 21, 36, 57, 85, 121, 167, 228, 315, 449, 666, 1023, 1605, 2533, 3974, 6156, 9394, 14137, 21051, 31159, 46066, 68305, 101850, 152857, 230720, 349576, 530476, 804579, 1217951, 1838897, 2769267, 4161918, 6247570, 9375799
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OFFSET
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0,9
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LINKS
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FORMULA
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G.f.: (1-x)^2/(1-3*x+3*x^2-x^3-x^8). [corrected by Georg Fischer, Apr 17 2020]
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EXAMPLE
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a(10+1)=11 because C(10,0) + C(5,3) = 1+10 = 11.
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MATHEMATICA
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Table[Sum[Binomial[n - 5*k, 3*k], {k, 0, Floor[n/8]}], {n, 0, 50}] (* G. C. Greubel, Apr 09 2018 *)
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PROG
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(PARI) a(n) = sum(k=0, n\8, binomial(n-5*k, 3*k)); \\ Michel Marcus, Sep 05 2013
(PARI) lista(nn) = {my(x = xx + O(xx^nn)); gf = (1-x)^2/(1-3*x+3*x^2-x^3-x^8); for (i=0, nn-1, print1(polcoeff(gf, i, xx), ", ")); } \\ Michel Marcus, Sep 05 2013
(Magma) [(&+[Binomial(n-5*k, 3*k): k in [0..Floor(n/8)]]): n in [0..50]]; // G. C. Greubel, Apr 09 2018
(Sage) ((1-x)^2/(1-3*x+3*x^2-x^3-x^8)).series(x, 44).coefficients(x, sparse=False) # Stefano Spezia, Aug 19 2023
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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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Alexey Kistanov (plast(AT)solid.ru), Jan 05 2006
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EXTENSIONS
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STATUS
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approved
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