|
|
A108369
|
|
Coefficients of x/(1+3*x+3*x^2-x^3).
|
|
5
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
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
|
|
|
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(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
|
|
|
STATUS
|
approved
|
|
|
|