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 A186194 #24 Feb 20 2025 12:53:09
%S A186194 0,2,132,12432,1235432,123465432,12345765432,1234568765432,
%T A186194 123456798765432,12345679098765432,1234567902098765432,
%U A186194 123456790132098765432,12345679012432098765432,1234567901235432098765432,123456790123465432098765432
%N A186194 a(n) = A002275(n) * (A002275(n)+1).
%C A186194 a(1),a(2),a(3),a(4),a(5) are (between the two 0's) the cores of the decimal expansions of a(10),a(11),a(12),a(13),a(14).
%C A186194 First differences begin 130,12300,1223000,122230000,....
%H A186194 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (111,-1110,1000).
%F A186194 a(n) = 2*A003555(n+1).
%F A186194 n 1's followed by n 8's is b(n)=18,1188,111888,11118888,1111188888, ...; then a(n)=b(n)/9. See its "contrary" A184337(n+1).
%F A186194 G.f.: 2*x*(-1+45*x) / ( (x-1)*(100*x-1)*(10*x-1) ). - _R. J. Mathar_, Mar 10 2011
%e A186194 a(1)=1*2=2, a(2)=11*12=132, a(3)=111*112=12432.
%t A186194 LinearRecurrence[{111,-1110,1000},{0,2,132},20] (* _Harvey P. Dale_, Apr 08 2022 *)
%K A186194 nonn,easy
%O A186194 0,2
%A A186194 _Paul Curtz_, Feb 14 2011
%E A186194 Zero added by _Franklin T. Adams-Watters_, Mar 09 2011