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A147841
a(n) = 11*a(n-1) - 9*a(n-2) with a(0)=1, a(1)=9.
5
1, 9, 90, 909, 9189, 92898, 939177, 9494865, 95990922, 970446357, 9810991629, 99186890706, 1002756873105, 10137643587801, 102489267607866, 1036143151396317, 10475171256888693, 105901595463208770, 1070641008783298233, 10823936737447401633, 109427535032871733866, 1106287454724562457829, 11184314186674341431325
OFFSET
0,2
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
Cf. A147703, A190872, A333344, A333345 (growth power).
Sequence in context: A173480 A052268 A155199 * A036258 A098399 A264914
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