This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A332126 #14 Jul 13 2024 17:30:25
%S A332126 6,262,22622,2226222,222262222,22222622222,2222226222222,
%T A332126 222222262222222,22222222622222222,2222222226222222222,
%U A332126 222222222262222222222,22222222222622222222222,2222222222226222222222222,222222222222262222222222222,22222222222222622222222222222,2222222222222226222222222222222
%N A332126 a(n) = 2*(10^(2n+1)-1)/9 + 4*10^n.
%H A332126 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (111,-1110,1000).
%F A332126 a(n) = 2*A138148(n) + 6*10^n = A002276(2n+1) + 4*10^n = 2*A332113(n).
%F A332126 G.f.: (6 - 404*x + 200*x^2)/((1 - x)(1 - 10*x)(1 - 100*x)).
%F A332126 a(n) = 111*a(n-1) - 1110*a(n-2) + 1000*a(n-3) for n > 2.
%F A332126 E.g.f.: 2*exp(x)*(10*exp(99*x) + 18*exp(9*x) - 1)/9. - _Stefano Spezia_, Jul 13 2024
%p A332126 A332126 := n -> 2*(10^(2*n+1)-1)/9+4*10^n;
%t A332126 Array[2 (10^(2 # + 1)-1)/9 + 4*10^# &, 15, 0]
%t A332126 Table[FromDigits[Join[PadRight[{},n,2],{6},PadRight[{},n,2]]],{n,0,20}] (* or *) LinearRecurrence[{111,-1110,1000},{6,262,22622},20] (* _Harvey P. Dale_, Oct 17 2021 *)
%o A332126 (PARI) apply( {A332126(n)=10^(n*2+1)\9*2+4*10^n}, [0..15])
%o A332126 (Python) def A332126(n): return 10**(n*2+1)//9*2+4*10**n
%Y A332126 Cf. A002275 (repunits R_n = (10^n-1)/9), A002276 (2*R_n), A011557 (10^n).
%Y A332126 Cf. A138148 (cyclops numbers with binary digits), A002113 (palindromes).
%Y A332126 Cf. A332116 .. A332196 (variants with different repeated digit 1, ..., 9).
%Y A332126 Cf. A332120 .. A332129 (variants with different middle digit 0, ..., 9).
%K A332126 nonn,base,easy
%O A332126 0,1
%A A332126 _M. F. Hasler_, Feb 09 2020