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A332196 a(n) = 10^(2n+1) - 1 - 3*10^n.

%I A332196 #18 Jul 13 2024 20:25:45
%S A332196 6,969,99699,9996999,999969999,99999699999,9999996999999,
%T A332196 999999969999999,99999999699999999,9999999996999999999,
%U A332196 999999999969999999999,99999999999699999999999,9999999999996999999999999,999999999999969999999999999,99999999999999699999999999999
%N A332196 a(n) = 10^(2n+1) - 1 - 3*10^n.
%H A332196 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (111,-1110,1000).
%F A332196 a(n) = 9*A138148(n) + 6*10^n.
%F A332196 G.f.: (6 + 303*x - 1200*x^2)/((1 - x)(1 - 10*x)(1 - 100*x)).
%F A332196 a(n) = 111*a(n-1) - 1110*a(n-2) + 1000*a(n-3) for n > 2.
%F A332196 E.g.f.: exp(x)*(10*exp(99*x) - 3*exp(9*x) - 1). - _Stefano Spezia_, Jul 13 2024
%p A332196 A332196 := n -> 10^(n*2+1)-1-3*10^n;
%t A332196 Array[ 10^(2 # + 1) - 1 - 3*10^# &, 15, 0]
%t A332196 FromDigits/@Table[Join[PadLeft[{6},n,9],PadRight[{},n-1,9]],{n,30}] (* or *) LinearRecurrence[{111,-1110,1000},{6,969,99699},30] (* _Harvey P. Dale_, May 03 2021 *)
%o A332196 (PARI) apply( {A332196(n)=10^(n*2+1)-1-3*10^n}, [0..15])
%o A332196 (Python) def A332196(n): return 10**(n*2+1)-1-3*10^n
%Y A332196 Cf. A002275 (repunits R_n = (10^n-1)/9), A002283 (9*R_n), A011557 (10^n).
%Y A332196 Cf. A138148 (cyclops numbers with binary digits only), A002113 (palindromes).
%Y A332196 Cf. A332116 .. A332186 (variants with different repeated digit 1, ..., 8).
%Y A332196 Cf. A332190 .. A332197, A181965 (variants with different middle digit 0, ..., 8).
%K A332196 nonn,base,easy
%O A332196 0,1
%A A332196 _M. F. Hasler_, Feb 08 2020