OFFSET
1,3
COMMENTS
The two ones at the start of the parent sequence represent parent and child 1-tuples in the grandparent sequence [(1) and (2) respectively], hence this sequence also starts with 1, 1 rather than 2, which would otherwise be a more sensible way to describe the pair of ones.
All other elements are effectively run-lengths of strings of the same integer in A229895.
The first occurrence of an integer, n, in the parent sequence, is the first of a run of n^n elements of value n. For later occurrences, the run length is n^k-(n-1)^k where k is the size of the k-tuple in the grandparent sequence, A229873.
The elements can be arranged into a triangle thus:
.... 1
.... 1, 4
.... 1, 5, 27
.... 1, 7, 37, 256
.... 1, 9, 61, 369, 3125
.... etc.
where the n-th line is:
.... n^1-(n-1)^1, n^2-(n-1)^2, ..., n^(k-1)-(n-1)^(k-1), n^n; 1 <= k < n
The first terms, for sufficiently large n simplifying as:
.... 1, 2n-1, 3n^2-3n+1, 4n^3-6n^2+4n-1, etc.
LINKS
Carl R. White, Rows 1..44 for triangle, flattened
MAPLE
T := proc (n, k) if k < n then n^k-(n-1)^k elif k = n then n^n else end if end proc: for n to 12 do seq(T(n, k), k = 1 .. n) end do; # yields sequence in triangular form - Emeric Deutsch, Jan 30 2017
PROG
(bc) /* GNU bc */ for(n=1; n<=10; n++)for(p=1; p<=n; p++){if(p==n){t=n^n}else{t=n^p-(n-1)^p}; print t, ", "}; print "...\n"
CROSSREFS
KEYWORD
AUTHOR
Carl R. White, Oct 03 2013
STATUS
approved