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

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

Offset

0,2

Links

Table of n, a(n) for n=0..7.

Takashi Agoh and Horst Alzer, Mean Value Inequalities for Motzkin Numbers, J. Int. Seq., Vol. 24 (2021), Article 21.6.8.

Eric Weisstein's World of Mathematics, Motzkin Number

Formula

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

Crossrefs

Cf. A001006, A114490.

Sequence in context: A346629 A073565 A039657 * A275125 A264123 A304645

Adjacent sequences: A114470 A114471 A114472 * A114474 A114475 A114476

Keyword

nonn,base

Author

Eric W. Weisstein, Nov 30 2005

Extensions

Edited by Charles R Greathouse IV, Aug 05 2010

More terms from Eric Rowland, Oct 23 2015

Status

approved