OFFSET
0,2
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (-6,-7,-6,-1).
FORMULA
a(n+2) = - 5*a(n+1) - a(n) + (-1)^n*A109265(n+3).
a(n) = -6*a(n-1) - 7*a(n-2) - 6*a(n-3) - a(n-4) for n>3. - Colin Barker, Apr 30 2019
a(n) = (1/2)*(ChebyshevU(n, -5/2) + ChebyshevU(n, -1/2)). - G. C. Greubel, Jan 03 2023
MAPLE
seriestolist(series((1+3*x+x^2)/((x^2+5*x+1)*(x^2+x+1)), x=0, 25));
MATHEMATICA
LinearRecurrence[{-6, -7, -6, -1}, {1, -3, 12, -57}, 40] (* G. C. Greubel, Jan 03 2023 *)
PROG
(PARI) Vec((1+3*x+x^2)/((1+x+x^2)*(1+5*x+x^2)) + O(x^25)) \\ Colin Barker, Apr 30 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1+3*x+x^2)/((1+x+x^2)*(1+5*x+x^2)) )); // G. C. Greubel, Jan 03 2023
(SageMath)
def A110309(n): return (1/2)*(chebyshev_U(n, -5/2)+chebyshev_U(n, -1/2))
[A110309(n) for n in range(41)] # G. C. Greubel, Jan 03 2023
CROSSREFS
KEYWORD
easy,sign
AUTHOR
Creighton Dement, Jul 19 2005
STATUS
approved