A114473 - OEIS

%I #23 Oct 01 2021 22:21:30

%S 1,4,45,473,4766,47705,477113,4771203

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

%H 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 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MotzkinNumber.html">Motzkin Number</a>

%F 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 Cf. A001006, A114490.

%K nonn,base

%O 0,2

%A _Eric W. Weisstein_, Nov 30 2005

%E Edited by _Charles R Greathouse IV_, Aug 05 2010

%E More terms from _Eric Rowland_, Oct 23 2015