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 A212704 a(n) = 9*n*10^(n-1). 13
 9, 180, 2700, 36000, 450000, 5400000, 63000000, 720000000, 8100000000, 90000000000, 990000000000, 10800000000000, 117000000000000, 1260000000000000, 13500000000000000, 144000000000000000, 1530000000000000000, 16200000000000000000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Main transitions in systems of n particles with spin 9/2. Please, refer to the general explanation in A212697. This particular sequence is obtained for base b=10, corresponding to spin S = (b-1)/2 = 9/2. Number of 0 needed to write all numbers of n+1 digits. - Bruno Berselli, Jun 30 2014 Essentially the same as A113119. - Bernard Schott, Nov 15 2022 From Bernard Schott, Nov 22 2022: (Start) Number of nonzero digits needed to write all integers from 1 up to 10^n - 1. a(n) is a square iff n in { A016754 union A033583\{0} } (see formulas). (End) LINKS Stanislav Sykora, Table of n, a(n) for n = 1..100 Stanislav Sýkora, Magnetic Resonance on OEIS, Stan's NMR Blog (Dec 31, 2014), Retrieved Nov 12, 2019. Index entries for linear recurrences with constant coefficients, signature (20,-100). FORMULA a(n) = n*(b-1)*b^(n-1) with b=10. From R. J. Mathar, Oct 15 2013: (Start) G.f.: 9*x / (10*x-1)^2. a(n) = 9*A053541(n). (End) From Bernard Schott, Nov 14 2022: (Start) a(n+1) - a(n) = 9*A081045(n). a(n) = A113119(n) for n > 1. a(n) = A033713(n+1) - A033713(n) = A033714(n+1) - A033714(n). a(A016754(n)) = (3 * (2n+1) * 10^(2*n*(n+1)))^2. a(A033583(n)) = (3 * n * 10^(5*n^2))^2. (End) MATHEMATICA Rest@ CoefficientList[Series[9 x/(10 x - 1)^2, {x, 0, 18}], x] (* or *) Array[9 # 10^(# - 1) &, 18] (* Michael De Vlieger, Nov 18 2019 *) PROG (PARI) mtrans(n, b) = n*(b-1)*b^(n-1); a(n) = mtrans(n, 10); (Python) def a(n): return 9*n*10**(n-1) print([a(n) for n in range(1, 21)]) # Michael S. Branicky, Nov 14 2022 CROSSREFS Cf. A016754, A033583, A033713, A033714, A081045, A113119. Cf. A001787, A212697, A212698, A212699, A212700, A212701, A212702, A212703 (for b=2..9). Sequence in context: A034221 A034240 A163132 * A231726 A064332 A319798 Adjacent sequences: A212701 A212702 A212703 * A212705 A212706 A212707 KEYWORD nonn,easy AUTHOR Stanislav Sykora, May 25 2012 STATUS approved

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Last modified September 25 16:14 EDT 2023. Contains 365648 sequences. (Running on oeis4.)