

A255327


a(n) = 0 if n is in the infinite trunk of "numberofruns beanstalk" (one of the terms of A255056), otherwise number of nodes (including leaves and the node n itself) in that finite subtree of the beanstalk.


11



0, 1, 0, 1, 0, 1, 0, 1, 2, 1, 0, 1, 0, 1, 0, 1, 5, 1, 0, 1, 2, 1, 0, 1, 2, 1, 0, 1, 0, 1, 0, 1, 0, 1, 3, 1, 0, 1, 2, 1, 4, 1, 0, 1, 2, 1, 0, 1, 5, 1, 0, 1, 2, 1, 0, 1, 2, 1, 0, 1, 0, 1, 0, 1, 0, 1, 3, 1, 0, 1, 2, 1, 10, 1, 0, 1, 8, 1, 0, 1, 3, 1, 2, 1, 0, 1, 2, 1, 4, 1, 0, 1, 2, 1, 0, 1, 0, 1, 3, 1, 0, 1, 2, 1, 4, 1, 0, 1, 2, 1, 0, 1, 5, 1, 0, 1, 2, 1, 0
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OFFSET

0,9


COMMENTS

The edgerelation between nodes is given by A236840(child) = parent. a(n) = 1 + the size of transitive closure of all children emanating from the parent at n. For any n in A255056 this would be infinite, thus such n are marked with zeros.
Odd numbers are leaves, as there are no such k that A236840(k) were odd, thus a(2n+1) = 1.


LINKS

Antti Karttunen, Table of n, a(n) for n = 0..8590


FORMULA

a(2n+1) = 1, and for even numbers 2n, if A255339(n) = 1, then a(2n) = 0, otherwise, a(2n) = 1 + sum_{k = A091067(n) .. A255068(n)} a(k).


PROG

(Scheme, with memoizationmacro definec)
(definec (A255327 n) (cond ((odd? n) 1) ((= 1 (A255339 (/ n 2))) 0) (else (+ 1 (add A255327 (A091067 (/ n 2)) (A255068 (/ n 2)))))))
;; Auxiliary function add implements sum_{i=lowlim..uplim} intfun(i)
(define (add intfun lowlim uplim) (let sumloop ((i lowlim) (res 0)) (cond ((> i uplim) res) (else (sumloop (1+ i) (+ res (intfun i)))))))


CROSSREFS

Cf. A091067, A236840, A255056, A255068, A255328, A255329, A255330, A255339.
Cf. also A213727, A227643.
Sequence in context: A073068 A166006 A208769 * A255391 A255396 A116683
Adjacent sequences: A255324 A255325 A255326 * A255328 A255329 A255330


KEYWORD

nonn


AUTHOR

Antti Karttunen, Feb 21 2015


STATUS

approved



