OFFSET
0,3
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (7,-4).
FORMULA
a(n) = ((7/2 + 1/2*sqrt(33))^n - (7/2 - 1/2*sqrt(33))^n)/sqrt(33). - Giorgio Balzarotti, May 28 2011
G.f.: x/(1 - 7*x + 4*x^2). - Philippe Deléham, Oct 12 2011
MAPLE
seq( simplify(2^(n-1)*ChebyshevU(n-1, 7/4)), n=0..30); # G. C. Greubel, Dec 24 2019
MATHEMATICA
LinearRecurrence[{7, -4}, {0, 1}, 30]
Table[2^(n - 1) * ChebyshevU[n - 1, 7/4], {n, 0, 30}] (* G. C. Greubel, Dec 24 2019 *)
PROG
(PARI) vector(31, n, 2^(n-2)*polchebyshev(n-2, 2, 7/4) ) \\ G. C. Greubel, Dec 24 2019
(Magma) I:=[0, 1]; [n le 2 select I[n] else 7*Self(n-1) - 4*Self(n-2): n in [1..20]]; // G. C. Greubel, Dec 24 2019
(Sage) [2^(n-1)*chebyshev_U(n-1, 7/4) for n in (0..30)] # G. C. Greubel, Dec 24 2019
(GAP) a:=[0, 1];; for n in [3..30] do a[n]:=7*a[n-1]-4*a[n-2]; od; a; # G. C. Greubel, Dec 24 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Joseph Stephan Orlovsky, May 24 2011
STATUS
approved