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%I #12 Nov 12 2012 17:59:54
%S 0,0,0,0,1,0,0,1,3,0,0,0,1,3,0,4,0,0,1,0,0,1,3,0,4,0,0,1,4,0,0,2,0,3,
%T 1,0,0,0,1,3,0,4,0,0,1,4,0,0,2,0,3,1,0,4,0,0,2,0,37,0,0,110,0,3,0,1,0,
%U 0,1,3,0,4,0,0,1,4,0,0,2,0,3,1,0,4,0,0
%N a(n) = A014486-index for the n-th tendril of infinite beanstalk (A213730(n)), with the "lesser numbers to the right 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="/A218788/b218788.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 larger numbers go to the left, we obtain:
%e ..........
%e 29...28...
%e ..\./.....
%e ...25..24.
%e ....\./...
%e .....22...
%e ..........
%e and the binary tree
%e .......
%e .\./...
%e ..*....
%e ...\./.
%e ....*..
%e .......
%e is located as A014486(3) in the normal encoding order of binary trees, thus a(9)=3.
%o (Scheme with Antti Karttunen's memoization macro definec):
%o (define (A218788 n) (Aux_for218788 (A213730 n)))
%o (definec (Aux_for218788 n) (cond ((zero? (A079559 n)) 0) ((not (zero? (A213719 n))) -1) (else (A072764bi (Aux_for218788 (A213724 n)) (Aux_for218788 (A213723 n))))))
%Y These are the mirror-images of binary trees given in A218787, i.e. a(n) = A057163(A218787(n)). A218786 gives the sizes of these trees. Cf. A072764, A218610, A218611.
%K nonn
%O 1,9
%A _Antti Karttunen_, Nov 11 2012
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