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A365694
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G.f. satisfies A(x) = 1 + x^3*A(x)^2 / (1 - x*A(x)).
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2
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1, 0, 0, 1, 1, 1, 3, 6, 10, 20, 42, 84, 170, 354, 740, 1549, 3269, 6945, 14811, 31711, 68177, 147091, 318313, 690837, 1503351, 3279445, 7169907, 15708485, 34482475, 75830981, 167042763, 368548926, 814341362, 1801867812, 3992172298, 8855912464, 19668236110
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OFFSET
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0,7
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LINKS
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FORMULA
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a(n) = Sum_{k=0..floor(n/3)} binomial(n-2*k-1,n-3*k) * binomial(n-k+1,k) / (n-k+1).
G.f.: A(x) = 2/(1 + x + sqrt(1 + x*(-2 + x - 4*x^2))). - Vaclav Kotesovec, Sep 16 2023
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MATHEMATICA
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CoefficientList[Series[2/(1 + x + Sqrt[1 + x*(-2 + x - 4*x^2)]), {x, 0, 20}], x] (* Vaclav Kotesovec, Sep 16 2023 *)
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PROG
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(PARI) a(n) = sum(k=0, n\3, binomial(n-2*k-1, n-3*k)*binomial(n-k+1, k)/(n-k+1));
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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