A119374 A lower diagonal of pendular trinomial triangle A119369.

1, 3, 10, 36, 133, 501, 1918, 7440, 29180, 115522, 461044, 1852938, 7492846, 30464306, 124461782, 510696350, 2103708187, 8696498477, 36066269640, 150015248758, 625664295594, 2615929689642, 10962436020878, 46037427169060

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Formula

G.f.: A(x) = B(x)^3/(1+x - x*B(x)) = B(x)^3*G(x) = B(x)^2*H(x) = B(x)*I(x), where B(x) is g.f. of A119370, G(x) is g.f. of A119371, H(x) is g.f. of A119372 and I(x) is g.f. of A119373.

G.f.: 16*(1+x)/( ((1+x^2) +sqrt((1+x^2)^2-4*x*(1+x)))^3*(1+4*x+x^2 +sqrt((1+4*x+x^2)^2 - 4*x*(1+x)*(3+2*x))) ).

Mathematica

CoefficientList[Series[16*(1+x)/( ((1+x^2) +Sqrt[(1+x^2)^2 -4*x*(1+x)])^3*(1+4*x +x^2 +Sqrt[(1+4*x+x^2)^2 -4*x*(1+x)*(3+2*x)])), {x, 0, 30}], x] (* G. C. Greubel, Mar 16 2021 *)

Prog

(PARI) {a(n)=polcoeff(16*(1+x)/((1+x^2)+sqrt((1+x^2)^2-4*x*(1+x)+x*O(x^n)))^3 /(1+4*x+x^2 + sqrt((1+4*x+x^2)^2 - 4*x*(1+x)*(3+2*x)+x*O(x^n))), n)}
(Sage)
def A119374_list(prec):
    P.<x> = PowerSeriesRing(QQ, prec)
    return P( 16*(1+x)/( ((1+x^2) +sqrt((1+x^2)^2-4*x*(1+x)))^3*(1+4*x+x^2 +sqrt((1+4*x+x^2)^2 - 4*x*(1+x)*(3+2*x))) ) ).list()
A119374_list(30) # G. C. Greubel, Mar 16 2021
(Magma)
R<x>:=PowerSeriesRing(Rationals(), 30);
Coefficients(R!( 16*(1+x)/( ((1+x^2) +Sqrt((1+x^2)^2-4*x*(1+x)))^3*(1+4*x+x^2 +Sqrt((1+4*x+x^2)^2 - 4*x*(1+x)*(3+2*x))) ) )); // G. C. Greubel, Mar 16 2021

Crossrefs

Cf. A119369, A119370, A119371, A119372, A119373, A119375, A119376.

Sequence in context: A102871 A371842 A277287 * A371773 A272686 A126188

Adjacent sequences: A119371 A119372 A119373 * A119375 A119376 A119377

Keyword

nonn

Author

Paul D. Hanna, May 17 2006

Status

approved