OFFSET
0,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..990
Index entries for linear recurrences with constant coefficients, signature (11,-9).
FORMULA
a(n) = Sum_{k=0..n} A147703(n,k)*8^k.
G.f.: (1-2*x)/(1 -11*x +9*x^2).
a(n) = 9*A333344(n-1) = A190872(n+1) - 2*A190872(n) = A333344(n) - A190872(n). - Kevin Ryde, Apr 11 2020
a(n) = 3^n*(ChebyshevU(n, 11/6) - (2/3)*ChebyshevU(n-1, 11/6)). - G. C. Greubel, May 28 2020
E.g.f.: exp(11*x/2)*(85*cosh(sqrt(85)*x/2) + 7*sqrt(85)*sinh(sqrt(85)*x/2))/85. - Stefano Spezia, Mar 02 2023
MAPLE
A147841:= n-> simplify( 3^n*(ChebyshevU(n, 11/6) - (2/3)*ChebyshevU(n-1, 11/6)) ):
seq(A147841(n), n=0..25); # G. C. Greubel, May 28 2020
MATHEMATICA
Table[3^n*(ChebyshevU[n, 11/6] - (2/3)*ChebyshevU[n-1, 11/6]), {n, 0, 25}] (* G. C. Greubel, May 28 2020 *)
LinearRecurrence[{11, -9}, {1, 9}, 30] (* Harvey P. Dale, Feb 28 2023 *)
PROG
(PARI) a(n) = polcoeff(lift(('x-2)*Mod('x, 'x^2-11*'x+9)^n), 1); \\ Kevin Ryde, Apr 11 2020
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Philippe Deléham, Nov 14 2008
EXTENSIONS
Entries corrected by Paolo P. Lava, Nov 18 2008
Terms a(18) onward added by G. C. Greubel, May 28 2020
STATUS
approved