OFFSET
1,4
COMMENTS
Also the length of row n of A182162.
This seems to be simply the natural numbers, with the terms in A000325 repeated.
It appears a(n+1) is the number of distinct possible heights of binary trees with n nodes. The minimum height of an n node binary tree is A000523(n), the maximum height is n-1 and all intermediate heights are possible. This conjecture is therefore equivalent to the conjectured formulas. - Yuchun Ji, Mar 22 2021
Conjecture: Partial sums of A347523, thus a(n) is the number of nonpowers of 2 <= n-1, or with offset 0: a(n) is the number of nonpowers of 2 <= n. - Omar E. Pol, Sep 30 2021
LINKS
S. Wagner, Asymptotic enumeration of extensional acyclic digraphs, in Proceedings of the SIAM Meeting on Analytic Algorithmics and Combinatorics (ANALCO12).
FORMULA
Conjecture, for all n >= 3: a(n) = A083058(n-1) + 1 = n - 1 - A000523(n-1) = n - 1 - floor(log(2,n)). - Antti Karttunen, Aug 17 2013
Conjecture: a(1) = 0, a(n) = n - 1 - Sum_{i=1..n} sign(floor((n-1)/ 2^i)), n > 1. - Wesley Ivan Hurt, Feb 02 2014
Conjecture: a(n) = n - Sum_{k=0..n-2} A036987(k). - Paul Barry, Mar 07 2017
MAPLE
A001192 := proc(n) option remember: if(n=0)then return 1: fi: return add((-1)^(n-k-1)*binomial(2^k-k, n-k)*procname(k), k=0..n-1); end: A182162 := proc(n, l) local vl: vl := add((-1)^(k-l)*binomial(n, k)*binomial(k, l)*binomial(2^(n-k)-n+k, k)*k!*(n-k)!*A001192(n-k), k=l..n): return vl: end: A182220 := proc(n) local l: for l from n to 1 by -1 do if(A182162(n, l)>0)then break:fi:od: return l: end: seq(A182220(n), n=1..60);
CROSSREFS
KEYWORD
nonn
AUTHOR
Nathaniel Johnston, Apr 19 2012
STATUS
approved