A262697 - OEIS

A262697

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.

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

0,2

LINKS

Antti Karttunen, Table of n, a(n) for n = 0..17724

FORMULA

If A262693(n) = 1 [when n is in A259934],

then a(n) = 0,

otherwise, if A060990(n) = 0 [when n is one of the leaves, A045765],

then a(n) = 1,

otherwise:

a(n) = 1 + Sum_{k = A082284(n) .. A262686(n)} [A049820(k) = n] * a(k).

(In the last clause [ ] stands for Iverson bracket, giving as its result 1 only when A049820(k) = n, and 0 otherwise).

EXAMPLE

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.

PROG

(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))))))))

CROSSREFS

Cf. A000005, A045765, A049820, A060990, A082284, A259934, A262686, A262693.

Cf. A262679, A262522, A262695, A262696, A262890.

Cf. also A213727, A227643, A255327.

Sequence in context: A372064 A179641 A110993 * A237421 A087014 A176906

Adjacent sequences: A262694 A262695 A262696 * A262698 A262699 A262700

KEYWORD

nonn

AUTHOR

Antti Karttunen, Oct 04 2015

STATUS

approved