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 A212704 #69 May 14 2025 09:09:23
%S A212704 9,180,2700,36000,450000,5400000,63000000,720000000,8100000000,
%T A212704 90000000000,990000000000,10800000000000,117000000000000,
%U A212704 1260000000000000,13500000000000000,144000000000000000,1530000000000000000,16200000000000000000,171000000000000000000,1800000000000000000000
%N A212704 a(n) = 9*n*10^(n-1).
%C A212704 Main transitions in systems of n particles with spin 9/2.
%C A212704 Please, refer to the general explanation in A212697.
%C A212704 This particular sequence is obtained for base b=10, corresponding to spin S = (b-1)/2 = 9/2.
%C A212704 Number of 0 needed to write all numbers of n+1 digits. - _Bruno Berselli_, Jun 30 2014
%C A212704 Essentially the same as A113119. - _Bernard Schott_, Nov 15 2022
%C A212704 From _Bernard Schott_, Nov 22 2022: (Start)
%C A212704 Number of nonzero digits needed to write all integers from 1 up to 10^n - 1.
%C A212704 a(n) is a square iff n in { A016754 union A033583\{0} } (see formulas). (End)
%H A212704 Stanislav Sykora, <a href="/A212704/b212704.txt">Table of n, a(n) for n = 1..100</a>
%H A212704 Stanislav Sýkora, <a href="http://www.ebyte.it/stan/blog12to14.html#14Dec31">Magnetic Resonance on OEIS</a>, Stan's NMR Blog (Dec 31, 2014), Retrieved Nov 12, 2019.
%H A212704 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (20,-100).
%F A212704 a(n) = n*(b-1)*b^(n-1) with b=10.
%F A212704 From _R. J. Mathar_, Oct 15 2013: (Start)
%F A212704 G.f.: 9*x/(10*x-1)^2.
%F A212704 a(n) = 9*A053541(n). (End)
%F A212704 From _Bernard Schott_, Nov 14 2022: (Start)
%F A212704 a(n+1) - a(n) = 9*A081045(n).
%F A212704 a(n) = A113119(n) for n > 1.
%F A212704 a(n) = A033713(n+1) - A033713(n) = A033714(n+1) - A033714(n).
%F A212704 a(A016754(n)) = (3 * (2n+1) * 10^(2*n*(n+1)))^2.
%F A212704 a(A033583(n)) = (3 * n * 10^(5*n^2))^2. (End)
%F A212704 From _Elmo R. Oliveira_, May 13 2025: (Start)
%F A212704 E.g.f.: 9*x*exp(10*x).
%F A212704 a(n) = A008591(n)*A011557(n-1).
%F A212704 a(n) = 20*a(n-1) - 100*a(n-2) for n > 2. (End)
%t A212704 Rest@ CoefficientList[Series[9 x/(10 x - 1)^2, {x, 0, 18}], x] (* or *)
%t A212704 Array[9 # 10^(# - 1) &, 18] (* _Michael De Vlieger_, Nov 18 2019 *)
%o A212704 (PARI) mtrans(n, b) = n*(b-1)*b^(n-1);
%o A212704 a(n) = mtrans(n, 10);
%o A212704 (Python)
%o A212704 def a(n): return 9*n*10**(n-1)
%o A212704 print([a(n) for n in range(1, 21)]) # _Michael S. Branicky_, Nov 14 2022
%Y A212704 Cf. A008591, A011557, A016754, A033583, A033713, A033714, A053541, A081045, A113119.
%Y A212704 Cf. A001787, A212697, A212698, A212699, A212700, A212701, A212702, A212703 (for b=2..9).
%K A212704 nonn,easy
%O A212704 1,1
%A A212704 _Stanislav Sykora_, May 25 2012