%I #10 Jul 13 2024 17:50:29

%S 0,202,22022,2220222,222202222,22222022222,2222220222222,

%T 222222202222222,22222222022222222,2222222220222222222,

%U 222222222202222222222,22222222222022222222222,2222222222220222222222222,222222222222202222222222222,22222222222222022222222222222,2222222222222220222222222222222

%N a(n) = 2*(10^(2n+1)-1)/9 - 2*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) = 2*A138148(n) = A002276(2n+1) - 2*10^n.

%F G.f.: 2*x*(101 - 200*x)/((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.

%F E.g.f.: 2*exp(x)*(10*exp(99*x) - 9*exp(9*x) - 1)/9. - _Stefano Spezia_, Jul 13 2024

%p A332120 := n -> 2*((10^(2*n+1)-1)/9-10^n);

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

%o (PARI) apply( {A332120(n)=(10^(n*2+1)\9-10^n)*2}, [0..15])

%o (Python) def A332120(n): return (10**(n*2+1)//9-10**n)*2

%Y Cf. A002275 (repunits R_n = (10^n-1)/9), A002276 (2*R_n), A011557 (10^n).

%Y Cf. A138148 (cyclops numbers with binary digits), A002113 (palindromes).

%Y Cf. A332130 .. A332190 (variants with different repeated digit 3, ..., 9).

%Y Cf. A332121 .. A332129 (variants with different middle digit 1, ..., 9).

%K nonn,base,easy

%O 0,2

%A _M. F. Hasler_, Feb 09 2020