A sequence related to Lionel Levile's sequence?

[Floor en Lyanne van Lamoen]

Dear Seqfans,

I just submitted the following sequence:

%I A113676
%S A113675
1,2,3,3,4,4,4,5,5,5,6,6,6,6,7,7,7,7,8,8,8,8,9,9,9,9,9,10,10,10,10,10,11,11,1
1,11,11,12,12,12,12,12,12,13,13,13,13,13,13,14,14,14,14,14,14,15,15,15,15,15
,15,16,16,16,16,16,16,16,17,17,17,17,17,17,17,18,18,18,18,18,18,18,19,19,19,
19,19,19,19
%N A113675 Nondecreasing sequence in which a(n) describes how many times n+1
is in the sequence, with a(1)=1.
%C A113675 This sequence can be divided into rows forming a triangle as
follows: start with a(1)=1 as the first row. The row sum of row n-1 gives
the number of elements in row n. This triangle starts 1; 2; 3,3;
4,4,4,5,5,5; ...
The final elements of this row seem to form Lionel Levile's sequence
A014644, except that 2 isn't duplicate.
%e A113675 a(9)=5 so 10 appears five times in the sequence.
%O A113675 1
%K A113675 nonn,easy
%A A113675 Floor van Lamoen (fvlamoen at hotmail.com), Nov 04 2005

I cannot fully understand if indeed we find Lionel Levile's sequence as
described. Perhaps I am missing something.

Kind regards,
Floor.