A147841 a(n) = 11*a(n-1) - 9*a(n-2) with a(0)=1, a(1)=9.
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
Links
- G. C. Greubel, Table of n, a(n) for n = 0..990
- Index entries for linear recurrences with constant coefficients, signature (11,-9).
Programs
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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
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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 *) -
PARI
a(n) = polcoeff(lift(('x-2)*Mod('x,'x^2-11*'x+9)^n), 1); \\ Kevin Ryde, Apr 11 2020
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
Extensions
Entries corrected by Paolo P. Lava, Nov 18 2008
Terms a(18) onward added by G. C. Greubel, May 28 2020