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a(n) = 8*(10^(2n+1)-1)/9 - 5*10^n.
2

%I #9 Feb 11 2020 08:28:29

%S 3,838,88388,8883888,888838888,88888388888,8888883888888,

%T 888888838888888,88888888388888888,8888888883888888888,

%U 888888888838888888888,88888888888388888888888,8888888888883888888888888,888888888888838888888888888,88888888888888388888888888888,8888888888888883888888888888888

%N a(n) = 8*(10^(2n+1)-1)/9 - 5*10^n.

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (111,-1110,1000).

%F a(n) = 8*A138148(n) + 3*10^n = A002282(2n+1) - 5*10^n.

%F G.f.: (3 + 505*x - 1300*x^2)/((1 - x)(1 - 10*x)(1 - 100*x)).

%F a(n) = 111*a(n-1) - 1110*a(n-2) + 1000*a(n-3) for n > 2.

%p A332183 := n -> 8*(10^(2*n+1)-1)/9-5*10^n;

%t Array[8 (10^(2 # + 1)-1)/9 - 5*10^# &, 15, 0]

%o (PARI) apply( {A332183(n)=10^(n*2+1)\9*8-5*10^n}, [0..15])

%o (Python) def A332183(n): return 10**(n*2+1)//9*8-5*10**n

%Y Cf. A002275 (repunits R_n = (10^n-1)/9), A002282 (8*R_n), A011557 (10^n).

%Y Cf. A138148 (cyclops numbers with binary digits only).

%Y Cf. A332113 .. A332193 (variants with different repeated digit 1, ..., 9).

%Y Cf. A332180 .. A332189 (variants with different middle digit 0, ..., 9).

%K nonn,base,easy

%O 0,1

%A _M. F. Hasler_, Feb 08 2020