OFFSET
0,2
LINKS
Wikipedia, Chebyshev polynomials
Wikipedia, Resultant
Index entries for linear recurrences with constant coefficients, signature (14,-34,14,-1).
FORMULA
a(n)^2 = 4^n * Resultant(U(2*n,x), 1+2*x^2+1/2*x^4), where U(n,x) is a Chebyshev polynomial of the second kind and i = sqrt(-1).
G.f.: ((1-x)*(1-6*x+x^2))/(1-14*x+34*x^2-14*x^3+x^4).
a(n) = 14*a(n-1) - 34*a(n-2) + 14*a(n-3) - a(n-4) for n > 3.
MATHEMATICA
a[n_] := 2^n * Sqrt[Resultant[ChebyshevU[2*n, x/2], ChebyshevT[4, I*x/2], x]]; Array[a, 21, 0] (* Amiram Eldar, May 04 2021 *)
PROG
(PARI) a(n) = sqrtint(4^n*polresultant(polchebyshev(2*n, 2, x/2), 1+2*x^2+1/2*x^4))
(PARI) N=20; x='x+O('x^N); Vec(((1-x)*(1-6*x+x^2))/(1-14*x+34*x^2-14*x^3+x^4))
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Apr 15 2020
STATUS
approved