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A365694
G.f. satisfies A(x) = 1 + x^3*A(x)^2 / (1 - x*A(x)).
2
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
OFFSET
0,7
FORMULA
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
MATHEMATICA
CoefficientList[Series[2/(1 + x + Sqrt[1 + x*(-2 + x - 4*x^2)]), {x, 0, 20}], x] (* Vaclav Kotesovec, Sep 16 2023 *)
PROG
(PARI) a(n) = sum(k=0, n\3, binomial(n-2*k-1, n-3*k)*binomial(n-k+1, k)/(n-k+1));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Sep 16 2023
STATUS
approved