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URL: https://oeis.org/A155157

⇱ A155157 - OEIS

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A155157
a(n) = 10*a(n-1) + 10*a(n-2), with a(0)=1, a(1)=9, a(2)=99.
11
1, 9, 99, 1080, 11790, 128700, 1404900, 15336000, 167409000, 1827450000, 19948590000, 217760400000, 2377089900000, 25948503000000, 283255929000000, 3092044320000000, 33753002490000000, 368450468100000000
OFFSET
0,2
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)
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 *)
PROG
(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
(SageMath) [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
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.
Sequence in context: A116260 A103456 A002283 * A264005 A232943 A245927
KEYWORD
nonn
AUTHOR
Philippe Deléham, Jan 21 2009
STATUS
approved