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A262890 a(n) = total number of nodes in the finite subtrees branching from node n in the infinite trunk (A259934) of the tree generated by edge-relation A049820(child) = parent.

%I A262890 #12 Jul 18 2021 19:26:38
%S A262890 6,0,41,0,0,5,0,16,0,2,0,1,1,26,4,0,0,3,0,1,13,0,105,2,1,1,2,5,18,7,0,
%T A262890 0,0,1,3,3,0,0,5,0,4,13,2,7,0,0,7,6,1,0,0,0,53,0,0,0,90,1,0,5,0,2,0,1,
%U A262890 1,0,12,1,0,3,61,0,0,0,0,0,0,2,117,7,0,2,10,0,0,1,23,1,1,1,0,0,1,0,5,1,0,3,2,2,568,1,1,1,4,1,5,9,3,0,22,1,0,9,2,1,7,0,2,10,1,1,0
%N A262890 a(n) = total number of nodes in the finite subtrees branching from node n in the infinite trunk (A259934) of the tree generated by edge-relation A049820(child) = parent.
%H A262890 Antti Karttunen, <a href="/A262890/b262890.txt">Table of n, a(n) for n = 0..8107</a>
%F A262890 a(n) = Sum_{k = A082284(A259934(n)) .. A262686(A259934(n))} [A049820(k) = A259934(n)] * A262697(k).
%F A262890 (Here [ ] stands for Iverson bracket, giving as its result 1 only when A049820(k) = A259934(n), and 0 otherwise.)
%F A262890 Other identities. For all n >= 0:
%F A262890 a(n) = A262888(n) + A262889(n).
%o A262890 (Scheme)
%o A262890 (define (A262890 n) (let ((t (A259934 n))) (let loop ((s 0) (k (A262686 t))) (cond ((<= k t) s) ((= t (A049820 k)) (loop (+ s (A262697 k)) (- k 1))) (else (loop s (- k 1)))))))
%Y A262890 Cf. A000005, A049820, A082284, A259934, A262686, A262697, A262888, A262889.
%Y A262890 Cf. A262892 (positions of zeros).
%Y A262890 Cf. A262893 (partial sums).
%Y A262890 Cf. also A255330.
%K A262890 nonn
%O A262890 0,1
%A A262890 _Antti Karttunen_, Oct 04 2015