OFFSET
1,4
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..500
Index entries for linear recurrences with constant coefficients, signature (-1,-41).
FORMULA
a(n) = (-1)^(n-1)*(p^n - q^n)/(p-q), where p = (1 + sqrt(163)*i)/2, q = (1 - sqrt(163)*i)/2.
G.f.: x/(1 + x + 41*x^2). - Roger L. Bagula, Apr 18 2010
a(n) = -a(n-1) -41*a(n-2), with a(0) = 0, a(1) = -1. - G. C. Greubel, Mar 29 2021
MATHEMATICA
p:= (1 +Sqrt[163]*I)/2; q:= (1 -Sqrt[163]*I)/2; f[n_]:= (-1)^(n-1)*(p^n -q^n)/(p-q); Table[Simplify[f[n]], {n, 0, 30}] (* modified by G. C. Greubel, Mar 29 2021 *)
CoefficientList[Series[x/(1+x+41*x^2), {x, 0, 30}], x] (* Roger L. Bagula, Apr 18 2010; modified by G. C. Greubel, Mar 29 2021 *)
LinearRecurrence[{-1, -41}, {0, -1}, 30] (* G. C. Greubel, Mar 29 2021 *)
PROG
(Magma)
R<x>:=PowerSeriesRing(Rationals(), 30);
Coefficients(R!( x/(1+x+41*x^2) )); // G. C. Greubel, Mar 29 2021
(Sage)
def A141528_list(prec):
P.<x> = PowerSeriesRing(QQ, prec)
return P( x/(1+x+41*x^2) ).list()
a=A141528_list(31); a[1:] # G. C. Greubel, Mar 29 2021
CROSSREFS
KEYWORD
sign
AUTHOR
Roger L. Bagula, Aug 11 2008
EXTENSIONS
Edited by G. C. Greubel, Mar 29 2021
STATUS
approved