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
Harvey P. Dale, Table of n, a(n) for n = 0..1000
Vincent Thill, Radicaux et Ramanujan, April 2021, see c(n).
Index entries for linear recurrences with constant coefficients, signature (-3,-3,1).
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) = -3*a(n-1) - 3*a(n-2) + a(n-3).
a(-1-n) = A108368(n).
a(n+1) = (-1)^n * Sum_{k=0..floor(n/3)} (-2)^k * binomial(n+2,3*k+2). - Seiichi Manyama, Aug 05 2024
MATHEMATICA
CoefficientList[Series[x/(1+3x+3x^2-x^3), {x, 0, 40}], x] (* or *) LinearRecurrence[{-3, -3, 1}, {0, 1, -3}, 40] (* Harvey P. Dale, Jul 30 2024 *)
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
KEYWORD
sign
AUTHOR
Michael Somos, Jun 01 2005
STATUS
approved