|
%I #15 Nov 12 2012 18:00:21
%S 0,0,0,0,1,0,0,1,2,0,0,0,1,2,0,8,0,0,1,0,0,1,2,0,8,0,0,1,8,0,0,3,0,2,
%T 1,0,0,0,1,2,0,8,0,0,1,8,0,0,3,0,2,1,0,8,0,0,3,0,60,0,0,172,0,2,0,1,0,
%U 0,1,2,0,8,0,0,1,8,0,0,3,0,2,1,0,8,0,0
%N a(n) = A014486-index for the n-th tendril of infinite beanstalk (A213730(n)), with the "lesser numbers to the left side" construction.
%C "Tendrils" of the beanstalk are the finite side-trees sprouting from its infinite trunk (see A179016) at the numbers given by A213730.
%H A. Karttunen, <a href="/A218787/b218787.txt">Table of n, a(n) for n = 1..8727</a>
%H A. Karttunen, <a href="/A014486/a014486_1.pdf">Illustration of how binary trees (the second rightmost column) are encoded by A014486</a>
%e A213730(9)=22, and from that branches 24 and 25 (as both A011371(24)=A011371(25)=22) and while 24 is a leaf (in A055938) the other branch 25 further branches to two leaves (as both A011371(28)=A011371(29)=25).
%e When we construct a binary tree from this in such a fashion that the lesser numbers go to the left, we obtain:
%e ...........
%e ...28...29.
%e .....\./...
%e ..24..25...
%e ...\ /.....
%e ....22.....
%e ...........
%e and the binary tree
%e ........
%e ...\./..
%e ....*...
%e .\./....
%e ..*.....
%e ........
%e is located as A014486(2) in the normal encoding order of binary trees, thus a(9)=2.
%o (Scheme with _Antti Karttunen_'s memoization macro definec):
%o (define (A218787 n) (Aux_for218787 (A213730 n)))
%o (definec (Aux_for218787 n) (cond ((zero? (A079559 n)) 0) ((not (zero? (A213719 n))) -1) (else (A072764bi (Aux_for218787 (A213723 n)) (Aux_for218787 (A213724 n))))))
%Y These are the mirror-images of binary trees given in A218788, i.e. a(n) = A057163(A218788(n)). A218786 gives the sizes of these trees. Cf. A072764, A218609, A218611.
%K nonn
%O 1,9
%A _Antti Karttunen_, Nov 11 2012
|
