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A262697
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a(n)=0 if n is in A259934, otherwise number of nodes (including leaves and the node n itself) in that finite subtree whose root is n and edge-relation is defined by A049820(child) = parent.
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11
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0, 6, 0, 3, 2, 2, 0, 1, 1, 38, 3, 37, 0, 1, 2, 33, 2, 32, 0, 1, 1, 30, 0, 29, 1, 1, 3, 28, 1, 26, 0, 24, 2, 1, 0, 23, 1, 1, 16, 21, 1, 2, 0, 1, 2, 18, 0, 17, 13, 1, 1, 16, 1, 14, 0, 1, 1, 13, 0, 10, 11, 9, 0, 1, 1, 8, 1, 1, 1, 6, 0, 4, 10, 3, 1, 1, 23, 2, 0, 1, 2, 22, 4, 20, 9, 1, 3, 19, 1, 5, 0, 13, 2, 4, 0, 11, 8, 10, 1, 3, 1, 2, 0, 1, 6, 9, 0, 8, 1, 1, 2, 6, 1, 1, 0, 3, 1, 1, 0, 2, 5, 0, 12, 1
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OFFSET
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0,2
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LINKS
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FORMULA
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then a(n) = 0,
then a(n) = 1,
otherwise:
(In the last clause [ ] stands for Iverson bracket, giving as its result 1 only when A049820(k) = n, and 0 otherwise).
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EXAMPLE
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For n=1, its transitive closure (as defined by edge-relation A049820(child) = parent) is the union of {1} itself together with all its descendants, together {1, 3, 4, 5, 7, 8}. We see that there are no other nodes in a subtree whose root is 1, because A049820(3) = 3 - d(3) = 1, A049820(4) = 1, A049820(5) = 3, A049820(7) = 5, A049820(8) = 4 and both 7 and 8 are terms of A045765. Thus a(1) = 6.
For n=9, its transitive closure is {9, 11, 13, 15, 16, 17, 19, 21, 23, 24, 27, 29, 31, 33, 35, 36, 37, 39, 41, 43, 45, 47, 51, 53, 55, 57, 59, 61, 63, 64, 65, 67, 69, 71, 73, 75, 77, 79}, containing 38 terms, thus a(9) = 38.
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PROG
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(Scheme, with memoization-macro definec)
(definec (A262697 n) (cond ((= 1 (A262693 n)) 0) (else (let loop ((s 0) (k (A262686 n))) (cond ((<= k n) (+ 1 s)) ((= n (A049820 k)) (loop (+ s (A262697 k)) (- k 1))) (else (loop s (- k 1))))))))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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