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A114473 Number of decimal digits in the 10^n-th Motzkin number.

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%I A114473 #24 Feb 16 2025 08:32:59
%S A114473 1,4,45,473,4766,47705,477113,4771203
%N A114473 Number of decimal digits in the 10^n-th Motzkin number.
%H A114473 Takashi Agoh and Horst Alzer, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL24/Alzer/alzer8.html">Mean Value Inequalities for Motzkin Numbers</a>, J. Int. Seq., Vol. 24 (2021), Article 21.6.8.
%H A114473 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MotzkinNumber.html">Motzkin Number</a>
%F A114473 Lim_{n->oo} log_10(a(n))/n = log_10(3) = 0.477121254719662437295027903... since the real root possessing the smallest absolute value of expression (1-2*x-3*x^2) (found in the g.f.) equals 1/3. - _Paul D. Hanna_, Dec 01 2005
%Y A114473 Cf. A001006, A114490.
%K A114473 nonn,base
%O A114473 0,2
%A A114473 _Eric W. Weisstein_, Nov 30 2005
%E A114473 Edited by _Charles R Greathouse IV_, Aug 05 2010
%E A114473 More terms from _Eric Rowland_, Oct 23 2015