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A122448 A lower diagonal of pendular trinomial triangle A122445. 8
1, 1, 3, 10, 36, 135, 525, 2094, 8524, 35266, 147862, 626884, 2682940, 11575707, 50295809, 219879814, 966487380, 4268781902, 18936044682, 84326759820, 376853237480, 1689551241606, 7597003401186, 34251504489484 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
FORMULA
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)).
MATHEMATICA
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 *)
PROG
(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)
def A122447_list(prec):
P.<x> = PowerSeriesRing(QQ, prec)
return P( 2/(1-x+2*x^2+2*x^3 +(1+x)*f(x)) ).list()
A122447_list(30) # G. C. Greubel, Mar 17 2021
(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
CROSSREFS
Sequence in context: A126188 A081909 A126189 * A007582 A369436 A026854
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Sep 07 2006
STATUS
approved

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Last modified March 28 22:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)