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 A138365 #15 Oct 15 2024 05:15:04 %S A138365 10,99,1090,11880,129601,1413720,15421330,168220899,1835008570, %T A138365 20016873360,218350598401,2381839709040,25981886201050, %U A138365 283418908502499,3091626107326450,33724468272088440,367877524885646401,4012928305470021960,43774333835284595170,477504743882660524899,5208777848873981178730 %N A138365 a(n) = A006190(n) * A006190(n+2). %C A138365 1/3 = 3/10 + 3/99 + 3/1090, + 3/11880 + ..., = 3/(1*10) + 3/(3*33) + 3/(10*109) + 3/(33*360) + ... %C A138365 Odd n terms == 1 mod 9; even n terms == 0 mod 9 %F A138365 a(n) = A006190(n) * A006190(n+2). %F A138365 Empirical g.f.: -x*(x-10) / ((x+1)*(x^2-11*x+1)). - _Colin Barker_, Oct 20 2013 %F A138365 For n >= 4, a(n) = 10*a(n-1) + 10*a(n-2) - a(n-3); from this it follows that the conjectured generating function is correct. - _Sela Fried_, Oct 14 2024 %e A138365 a(3) = A006190(3) * A006190(5) = 10 * 109 = 1090. %Y A138365 Cf. A006190. %K A138365 nonn %O A138365 1,1 %A A138365 _Gary W. Adamson_, Mar 16 2008