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A122448
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A lower diagonal of pendular trinomial triangle A122445.
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8
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1, 1, 3, 10, 36, 135, 525, 2094, 8524, 35266, 147862, 626884, 2682940, 11575707, 50295809, 219879814, 966487380, 4268781902, 18936044682, 84326759820, 376853237480, 1689551241606, 7597003401186, 34251504489484
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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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G.f.: A(x) = B(x)/(1 +x -x*B(x) ) where B(x) is the g.f. of A122446.
G.f. satisfies: A(x) = 1 + x*(1-2*x-2*x^2)*A(x) + x^2*(4+3*x)*A(x)^2.
G.f.: A(x) = 2/(1 -x +2*x^2 +2*x^3 + (1+x)*sqrt(1 -4*x -4*x^2 +4*x^4)).
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MATHEMATICA
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f[x_]:= Sqrt[1-4*x-4*x^2+4*x^4];
CoefficientList[Series[2/(1-x+2*x^2+2*x^3 +(1+x)*f[x]), {x, 0, 30}], x] (* G. C. Greubel, Mar 17 2021 *)
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PROG
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(PARI) {a(n) =polcoeff(2/(1-x+2*x^2+2*x^3 +(1+x)*sqrt(1-4*x-4*x^2+4*x^4 +x*O(x^n) )), n)}
(Sage)
def f(x): return sqrt(1-4*x-4*x^2+4*x^4)
P.<x> = PowerSeriesRing(QQ, prec)
return P( 2/(1-x+2*x^2+2*x^3 +(1+x)*f(x)) ).list()
(Magma)
R<x>:=PowerSeriesRing(Rationals(), 30);
f:= func< x | Sqrt(1-4*x-4*x^2+4*x^4) >;
Coefficients(R!( 2/(1-x+2*x^2+2*x^3 +(1+x)*f(x)) )); // G. C. Greubel, Mar 17 2021
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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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