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

0,2

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

Cf. A147703, A190872, A333344, A333345 (growth power).

Sequence in context: A173480 A052268 A155199 * A036258 A098399 A264914

Adjacent sequences: A147838 A147839 A147840 * A147842 A147843 A147844

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