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 A332154 #10 Mar 09 2025 18:04:16
%S A332154 4,545,55455,5554555,555545555,55555455555,5555554555555,
%T A332154 555555545555555,55555555455555555,5555555554555555555,
%U A332154 555555555545555555555,55555555555455555555555,5555555555554555555555555,555555555555545555555555555,55555555555555455555555555555,5555555555555554555555555555555
%N A332154 a(n) = 5*(10^(2*n+1)-1)/9 - 10^n.
%H A332154 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (111,-1110,1000).
%F A332154 a(n) = 5*A138148(n) + 4*10^n = A002279(2n+1) - 10^n.
%F A332154 G.f.: (4 + 101*x - 600*x^2)/((1 - x)(1 - 10*x)(1 - 100*x)).
%F A332154 a(n) = 111*a(n-1) - 1110*a(n-2) + 1000*a(n-3) for n > 2.
%p A332154 A332154 := n -> 5*(10^(2*n+1)-1)/9-10^n;
%t A332154 Array[5 (10^(2 # + 1)-1)/9 - 10^# &, 15, 0]
%t A332154 LinearRecurrence[{111,-1110,1000},{4,545,55455},20] (* or *) Table[FromDigits[Join[PadRight[{},n,5],{4},PadRight[{},n,5]]],{n,0,20}] (* _Harvey P. Dale_, Mar 09 2025 *)
%o A332154 (PARI) apply( {A332154(n)=10^(n*2+1)\9*5-10^n}, [0..15])
%o A332154 (Python) def A332154(n): return 10**(n*2+1)//9*5-10**n
%Y A332154 Cf. A002275 (repunits R_n = (10^n-1)/9), A002279 (5*R_n), A011557 (10^n).
%Y A332154 Cf. A138148 (cyclops numbers with binary digits), A002113 (palindromes).
%Y A332154 Cf. A332114 .. A332194 (variants with different repeated digit 1, ..., 9).
%Y A332154 Cf. A332150 .. A332159 (variants with different middle digit 0, ..., 9).
%K A332154 nonn,base,easy
%O A332154 0,1
%A A332154 _M. F. Hasler_, Feb 09 2020