A108369 Coefficients of x/(1+3*x+3*x^2-x^3).

0, 1, -3, 6, -8, 3, 21, -80, 180, -279, 217, 366, -2028, 5203, -9159, 9840, 3160, -48159, 144837, -286874, 377952, -128397, -1035539, 3869760, -8631060, 13248361, -9982143, -18429714, 98483932, -250144797, 436552881, -460740320, -177582480, 2351521281

Offset

0,3

References

L. E. Dickson, History of the Theory of Numbers. Carnegie Institute Public. 256, Washington, DC, Vol. 1, 1919; Vol. 2, 1920; Vol. 3, 1923, see vol. 2, p. 562.

Links

Table of n, a(n) for n=0..33.

Vincent Thill, Radicaux et Ramanujan, April 2021, see c(n).

Formula

x=a(n), z=a(-n-2), y=a(n)+a(n+1), t=a(-1-n)+a(-n-2) is a solution to 2(x^3+z^3)=y^3+t^3.

G.f.: x/(1+3*x+3*x^2-x^3). a(n)=-3a(n-1)-3a(n-2)+a(n-3). a(-1-n)=A108368(n).

Prog

(PARI) {a(n)=if(n>=0, polcoeff(x/(1+3*x+3*x^2-x^3)+x*O(x^n), n), n=-1-n; polcoeff(x/(1-3*x-3*x^2-x^3)+x*O(x^n), n))}

Crossrefs

Sequence in context: A278498 A011334 A200340 * A010621 A258232 A296568

Adjacent sequences: A108366 A108367 A108368 * A108370 A108371 A108372

Keyword

sign

Author

Michael Somos, Jun 01 2005

Status

approved