OFFSET
0,3
COMMENTS
Hankel transform of A091526.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (-2,-9,-8,-16).
FORMULA
G.f.: (1 +2*x)/(1 +2*x +9*x^2 +8*x^3 +16*x^4).
a(n) = (-2)*Sum_{j=0..n} ChebyshevU(n-j, 1/4)*(ChebyshevU(j, 1/4) - ChebyshevU(j-1, 1/4)). - G. C. Greubel, Jan 28 2022
MATHEMATICA
LinearRecurrence[{-2, -9, -8, -16}, {1, 0, -9, 10}, 41] (* or *)
A156857[n_]:= (-2)^n*Sum[ChebyshevU[n-j, 1/4]*(ChebyshevU[j, 1/4] - ChebyshevU[j-1, 1/4]), {j, 0, n}];
Table[A156857[n], {n, 0, 40}] (* G. C. Greubel, Jan 28 2022 *)
PROG
(Magma) I:=[1, 0, -9, 10]; [n le 4 select I[n] else (-1)*(2*Self(n-1) +9*Self(n-2) +8*Self(n-3) +16*Self(n-4)): n in [1..41]]; // G. C. Greubel, Jan 28 2022
(Sage)
def A156857(n): return (-2)^n*sum( chebyshev_U(n-j, 1/4)*(chebyshev_U(j, 1/4) - chebyshev_U(j-1, 1/4)) for j in (0..n))
[A156857(n) for n in (0..40)] # G. C. Greubel, Jan 28 2022
CROSSREFS
KEYWORD
easy,sign
AUTHOR
Paul Barry, Feb 17 2009
STATUS
approved