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a(n) = a(n-1) + 10*a(n-2) for n >= 2, a(0)=1, a(1)=2.
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%I #30 Jan 02 2024 08:55:13

%S 1,2,12,32,152,472,1992,6712,26632,93752,360072,1297592,4898312,

%T 17874232,66857352,245599672,914173192,3370169912,12511901832,

%U 46213600952,171332619272,633468628792,2346794821512,8681481109432

%N a(n) = a(n-1) + 10*a(n-2) for n >= 2, a(0)=1, a(1)=2.

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (1,10).

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

%F a(n) = Sum_{k=0..n+1} A122950(n+1,k)*9^(n+1-k). - _Philippe Deléham_, Jan 08 2008

%t LinearRecurrence[{1, 10}, {1, 2}, 24] (* or *)

%t CoefficientList[Series[(1 + x)/(1 - x - 10 x^2), {x, 0, 23}], x] (* _Michael De Vlieger_, Jul 20 2017 *)

%K easy,nonn

%O 0,2

%A _Philippe Deléham_, Jan 03 2008