Levine's sequence is the integer sequence formed by the final terms of recursively constructed rows. Start with the row . If a row is , the next row contains copies of 1, followed by copies of 2, continuing through copies of (Sloane 1999, Numberphile 2021). Thus the first three rows
are ,
, and , and the first terms of Levine's sequence are 1, 2,
2, 3, 4, 7, 14, 42, 213, 2837, 175450, ... (OEIS A011784).
If
is the last term in row , then is the number of elements in row . The number of elements in row is the sum of the elements in row
, so is that row sum (Sloane 1999).
Numberphile. "The Levine Sequence." Mar. 31, 2021. https://www.youtube.com/watch?v=KNjPPFyEeLo.Sloane,
N. J. A. "My Favorite Integer Sequences." In Sequences and
Their Applications: Proceedings of SETA '98 (Ed. C. Ding, T. Helleseth,
and H. Niederreiter). London, England: Springer-Verlag, pp. 103-130, 1999.
https://doi.org/10.1007/978-1-4471-0551-0_7.Sloane,
N. J. A. Sequence A011784 in "The
On-Line Encyclopedia of Integer Sequences."
. If a row is 
, the next row contains 
copies of 1, followed by 
copies of 2, continuing through 
copies of 
(Sloane 1999, Numberphile 2021). Thus the first three rows
are 
,
, and 
, and the first terms of Levine's sequence are 1, 2,
2, 3, 4, 7, 14, 42, 213, 2837, 175450, ... (OEIS A011784).
is the last term in row 
, then 
is the number of elements in row 
. The number of elements in row 
is the sum of the elements in row
, so 
is that row sum (Sloane 1999).
