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) - A099837(n+1).
a(n) + a(n+1) + a(n+2) = A002320(n).
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) = (1/4)*(3*U(n,-5/2) + U(n-1,-5/2) + U(n,-1/2) - U(n-1,-1/2)), where U(n, x) = ChebyshevU(n, x). - G. C. Greubel, Jan 03 2023
MAPLE
seriestolist(series((1+2*x)/((x^2+x+1)*(x^2+5*x+1)), x=0, 25));
MATHEMATICA
LinearRecurrence[{-6, -7, -6, -1}, {1, -4, 17, -80}, 41] (* G. C. Greubel, Jan 03 2023 *)
PROG
(PARI) Vec((1+2*x)/((1+x+x^2)*(1+5*x+x^2)) + O(x^25)) \\ Colin Barker, Apr 30 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+2*x)/((1+x+x^2)*(1+5*x+x^2)) )); // G. C. Greubel, Jan 03 2023
(SageMath)
def U(n, x): return chebyshev_U(n, x)
def A110307(n): return (1/4)*(3*U(n, -5/2) +U(n-1, -5/2) +U(n, -1/2) -U(n-1, -1/2))
[A110307(n) for n in range(41)] # G. C. Greubel, Jan 03 2023
CROSSREFS
KEYWORD
easy,sign
AUTHOR
Creighton Dement, Jul 19 2005
STATUS
approved