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a(n) = ((10-sqrt(10))^n + (10+sqrt(10))^n) / 2.
4

%I #11 Jul 06 2017 10:30:13

%S 1,10,110,1300,16100,205000,2651000,34570000,452810000,5944900000,

%T 78145100000,1027861000000,13524161000000,177975730000000,

%U 2342340110000000,30828986500000000,405769120100000000,5340773617000000000,70296251531000000000,925255405090000000000

%N a(n) = ((10-sqrt(10))^n + (10+sqrt(10))^n) / 2.

%H Colin Barker, <a href="/A289414/b289414.txt">Table of n, a(n) for n = 0..850</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (20,-90).

%F G.f.: (1 - 10*x) / (1 - 20*x + 90*x^2).

%F a(n) = 20*a(n-1) - 90*a(n-2) for n>1.

%p a:= n-> (<<0|1>, <-90|20>>^n. <<1,10>>)[1,1]:

%p seq(a(n), n=0..25); # _Alois P. Heinz_, Jul 06 2017

%o (PARI) Vec((1 - 10*x) / (1 - 20*x + 90*x^2) + O(x^25))

%Y Cf. A083881, A090139, A143079, A145301, A145302, A145303, A289415.

%K nonn,easy

%O 0,2

%A _Colin Barker_, Jul 06 2017