OFFSET
1,3
COMMENTS
Can be generated recursively by first setting R_1 = (1), after which each R_n is obtained by replacing in R_{n-1} each term k with terms 1 .. k, followed by final n. This sequence is then obtained by concatenating all levels R_1, R_2, ..., R_inf together. See page 230 in Kubo-Vakil paper (page 6 in PDF).
Deleting all 1's and decrementing the remaining terms by one gives the sequence back.
Comment from N. J. A. Sloane, Nov 05 2017: (Start)
The following simple Pascal-like triangle produces the same sequence. Construct a triangle T(n,k) of strings (with 0 <= k <= n), where T(0,0) = {1}, T(n,n) = {n+1}, and otherwise T(n,k) is the concatenation of T(n-1,k-1) and T(n-1,k). The first few rows of the triangle (where the strings T(n,k) are shown without spaces for legibility) are:
1
1,2
1,12,3
1,112,123,4
1,1112,112123,1234,5
1,11112,1112112123,1121231234,12345,6
...
Now read the strings across the rows to get the sequence. T(n,k) has length binomial(n,k). (End)
LINKS
Antti Karttunen, Table of n, a(n) for n = 1..8191
T. Kubo and R. Vakil, On Conway's recursive sequence, Discr. Math. 152 (1996), 225-252.
FORMULA
EXAMPLE
Illustration of the sequence as a tree:
1
/ \
1 2
/ /|\
1 1 2 3_________
/ / /| | \ \ \
1 1 1 2 1 2 3__ 4________
/ / / /| | / \ |\ \ \ \ \ \ \
1 1 1 1 2 1 1 2 1 2 3 1 2 3 4 5
etc.
Compare with the illustration in A265332.
PROG
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jan 10 2016
STATUS
approved