A122449 A lower diagonal of pendular trinomial triangle A122445.

1, 2, 6, 22, 83, 324, 1298, 5302, 22002, 92488, 392996, 1685232, 7283511, 31694460, 138746706, 610601374, 2699835614, 11988069480, 53433418716, 238986495540, 1072250526558, 4824638825032, 21765895919444, 98433111857436

Offset

0,2

Links

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

Formula

G.f.: A(x) = B(x)^2/(1+x -x*B(x)) where B(x) is the g.f. of A122446.

G.f.: 2/(1 -2*x -2*x^2 -2*x^3 +4*x^4 +4*x^5 +(1 +2*x^2 +2*x^3)*f(x)), where f(x) = sqrt(1 -4*x -4*x^2 +4*x^4). - G. C. Greubel, Mar 17 2021

Mathematica

f[x_] := Sqrt[1 - 4*x - 4*x^2 + 4*x^4];
CoefficientList[Series[2/(1-2*x-2*x^2-2*x^3+4*x^4+4*x^5 +(1+2*x^2+2*x^3)*f[x]), {x, 0, 30}], x] (* G. C. Greubel, Mar 17 2021 *)

Prog

(PARI) {a(n)=local(A, B=2/(1+2*x^2+sqrt(1-4*x-4*x^2+4*x^4+x^2*O(x^n)))); A=B^2/(1+x-x*B); polcoeff(A, n, x)}
(Sage)
def f(x): return sqrt(1-4*x-4*x^2+4*x^4)
def A122449_list(prec):
    P.<x> = PowerSeriesRing(QQ, prec)
    return P( 2/(1-2*x-2*x^2-2*x^3+4*x^4+4*x^5 +(1+2*x^2+2*x^3)*f(x)) ).list()
A122449_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/(1-2*x-2*x^2-2*x^3+4*x^4+4*x^5 +(1+2*x^2+2*x^3)*f(x)) )); // G. C. Greubel, Mar 17 2021

Crossrefs

Cf. A122445, A122446, A122447, A122448, A122450, A122451, A122452.

Sequence in context: A150236 A068946 A150237 * A150238 A150239 A150240

Adjacent sequences: A122446 A122447 A122448 * A122450 A122451 A122452

Keyword

nonn

Author

Paul D. Hanna, Sep 07 2006

Status

approved