A155157 a(n) = 10*a(n-1) + 10*a(n-2), with a(0)=1, a(1)=9, a(2)=99.

1, 9, 99, 1080, 11790, 128700, 1404900, 15336000, 167409000, 1827450000, 19948590000, 217760400000, 2377089900000, 25948503000000, 283255929000000, 3092044320000000, 33753002490000000, 368450468100000000

Offset: 0

Author

Philippe Deléham, Jan 21 2009

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..950
• Index entries for linear recurrences with constant coefficients, signature (10,10).

Crossrefs

Sequences of the form a(n) = m*(a(n-1) + a(n-2)) with a(0)=1, a(1) = m-1, a(2) = m^2 -1: A155020 (m=2), A155116 (m=3), A155117 (m=4), A155119 (m=5), A155127 (m=6), A155130 (m=7), A155132 (m=8), A155144 (m=9), this sequence (m=10).

Cf. A057093.

Programs

Magma

[1]cat[n le 2 select 9*(10*n-9) else 10*(Self(n-1) + Self(n-2)): n in [1..30]]; // G. C. Greubel, Mar 20 2021

Maple

1,seq( simplify(9*(-I*sqrt(10))^n*ChebyshevU(n, I*sqrt(10)/2)/10), n=1..30); # G. C. Greubel, Mar 20 2021

Mathematica

LinearRecurrence[{10,10},{1,9,99},20] (* Harvey P. Dale, Jan 27 2016 *)

Sage

[1]+[(9/10)*(-i*sqrt(10))^n*chebyshev_U(n, i*sqrt(10)/2) for n in (1..30)] # G. C. Greubel, Mar 20 2021

Formula

G.f.: (1-x-x^2)/(1-10*x-10*x^2).

From G. C. Greubel, Mar 20 2021: (Start)

a(n) = ([n=0] + 9*A057093(n))/10.

a(n) = (1/10)*([n=0] + 9*(-i*sqrt(10))^n*ChebyshevU(n, i*sqrt(10)/2)). (End)