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%I #14 Jan 19 2024 13:01:49
%S 3,939,99399,9993999,999939999,99999399999,9999993999999,
%T 999999939999999,99999999399999999,9999999993999999999,
%U 999999999939999999999,99999999999399999999999,9999999999993999999999999,999999999999939999999999999,99999999999999399999999999999,9999999999999993999999999999999
%N a(n) = 10^(2n+1) - 1 - 6*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) = 9*A138148(n) + 3*10^n = A002283(2n+1) - 6*10^n.
%F G.f.: (3 + 606*x - 1500*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 A332193 := n -> 10^(n*2+1)-1-6*10^n;
%t Array[ 10^(2 # + 1) - 1 - 6*10^# &, 15, 0]
%t LinearRecurrence[{111,-1110,1000},{3,939,99399},20] (* _Harvey P. Dale_, Jan 19 2024 *)
%o (PARI) apply( {A332193(n)=10^(n*2+1)-1-6*10^n}, [0..15])
%o (Python) def A332193(n): return 10**(n*2+1)-1-6*10^n
%Y Cf. A002275 (repunits R_n = (10^n-1)/9), A002283 (9*R_n), A011557 (10^n).
%Y Cf. A138148 (cyclops numbers with binary digits only), A002113 (palindromes).
%Y Cf. A332113 .. A332183 (variants with different repeated digit 1, ..., 8).
%Y Cf. A332190 .. A332197, A181965 (variants with different middle digit 0, ..., 8).
%K nonn,base,easy
%O 0,1
%A _M. F. Hasler_, Feb 08 2020
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