%I #24 Mar 03 2023 07:53:41

%S 1,10,101,1021,10322,104353,1054985,10665658,107827373,1090110181,

%T 11020765634,111417430345,1126404843089,11387696400874,

%U 115127016821813,1163907917432077,11766843940356530,118960112087033137,1202659637494155737

%N a(n) = 11*a(n-1) - 9*a(n-2) starting a(0)=1, a(1)=10.

%C First differences of A190872.

%H Kevin Ryde, <a href="/A333344/b333344.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (11,-9).

%F a(n) = A190872(n+1) - A190872(n) = A190872(n) + A147841(n).

%F G.f.: (1 - x)/(1 - 11*x + 9*x^2).

%F E.g.f.: exp(11*x/2)*(85*cosh(sqrt(85)*x/2) + 9*sqrt(85)*sinh(sqrt(85)*x/2))/85. - _Stefano Spezia_, Mar 03 2023

%t LinearRecurrence[{11, -9}, {1, 10}, 20] (* _Amiram Eldar_, Mar 15 2020 *)

%o (PARI) a(n) = polcoeff(lift(('x-1)*Mod('x,'x^2-11*'x+9)^n), 1);

%Y Cf. A333345 (growth power), A190872 (partial sums), A147841, A333347.

%K nonn,easy

%O 0,2

%A _Kevin Ryde_, Mar 15 2020