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A255330 a(n) = total number of nodes in the finite subtrees branching from the node n in the infinite trunk of "number-of-runs beanstalk" (A255056).

%I A255330 #10 Feb 21 2015 15:37:29
%S A255330 1,2,0,4,1,0,7,0,3,1,0,5,2,6,0,6,0,3,1,0,5,2,12,0,2,5,0,4,2,6,0,6,0,3,
%T A255330 1,0,5,2,12,0,2,7,1,12,4,0,2,5,0,4,2,12,0,2,5,0,4,2,6,0,6,0,3,1,0,5,2,
%U A255330 12,0,2,7,1,12,4,0,2,7,1,10,17,0,0,1,11,4,0,2,5,0,4,2,12,0,2,7,1,12,4,0,2,5,0,4,2,12,0,2,5,0,4,2,6,0,6,0,3,1,0,5
%N A255330 a(n) = total number of nodes in the finite subtrees branching from the node n in the infinite trunk of "number-of-runs beanstalk" (A255056).
%C A255330 A255058 gives the number of branches (children) of the node n in the trunk, of which one is the next node of the infinite trunk itself. Thus, if A255058(n) = 1, then a(n) = 0.
%H A255330 Antti Karttunen, <a href="/A255330/b255330.txt">Table of n, a(n) for n = 0..8590</a>
%F A255330 a(0) = 1; a(n) = sum_{k = A091067(A255057(n)) .. A255068(A255057(n))} A255327(k).
%F A255330 a(n) = A255328(n) + A255329(n).
%e A255330 The edge-relation between nodes is given by A236840(child) = parent. Odd numbers are leaves, as there are no such k that A236840(k) were odd.
%e A255330 The node 11 in the infinite trunk is A255056(11) = 30. Apart from 32 [we have A236840(32) = 30] which is the next node (node 12) in the infinite trunk, it has a single leaf-child 31 [A236840(31) = 30] at the "left side" (less than 32), and a leaf-child 33 [A236840(33) = 30] (more than 32) at the "right side", and also at that side, a subtree of three nodes 34 <- 38 <- 43 [we have A236840(43) = 38, A236840(38) = 34 and A236840(34) = 30], thus in total there are 1+1+3 = 5 nodes in finite branches emanating from the node 11 of the infinite trunk, and a(11) = 5.
%o A255330 (Scheme)
%o A255330 (define (A255330 n) (if (zero? n) 1 (let ((k (A255057 n))) (add A255327 (A091067 k) (A255068 k)))))
%o A255330 ;; Other code as in A255327.
%Y A255330 Partial sums: A255333.
%Y A255330 Cf. A091067, A236840, A255056, A255058, A255068, A255327, A255328, A255329, A255331.
%K A255330 nonn
%O A255330 0,2
%A A255330 _Antti Karttunen_, Feb 21 2015