A195105 E.g.f.: sqrt(cos(x)^6 + sin(x)^6).

1, -3, 21, 177, 11721, 605157, -13346979, -22645137063, -9383133860079, -3118216413426483, -681462248603151579, 220767331752698256897, 516670540464500515714521, 546555407869823056031953077, 418410321677501798899834234221, 139924678536116450478811178022057

Offset

1,2

Comments

The e.g.f. sqrt(cos(t)^6 + sin(t)^6) gives the distance from the origin to a point on the astroid (a 4-cusped hypocycloid) given by x^(2/3) + y^(2/3) = 1, using the parametric equations x = cos(t)^3 and y = sin(t)^3.

Links

Table of n, a(n) for n=1..16.

Example

E.g.f.: A(x) = 1 - 3*x^2/2! + 21*x^4/4! + 177*x^6/6! + 11721*x^8/8! +...
where A(x)^2 = cos(x)^6 + sin(x)^6, which begins:
A(x)^2 = 1 - 6*x^2/2! + 96*x^4/4! - 1536*x^6/6! + 24576*x^8/8! +...

Mathematica

With[{nn=30}, Take[CoefficientList[Series[Sqrt[Cos[x]^6+Sin[x]^6], {x, 0, nn}], x] Range[0, nn]!, {1, -1, 2}]] (* Harvey P. Dale, Jul 31 2020 *)

Prog

(PARI) {a(n)=local(X=x+x*O(x^(2*n))); n=2*n; n!*polcoeff(sqrt(cos(X)^6+sin(X)^6), n)}

Crossrefs

Sequence in context: A379086 A257675 A372108 * A285272 A295541 A369941

Adjacent sequences: A195102 A195103 A195104 * A195106 A195107 A195108

Keyword

sign

Author

Paul D. Hanna, Sep 09 2011

Status

approved