A230407 Absolute value of a(n) tells the size of the n-th side-tree ("tendril", A230430(n)) in the factorial beanstalk; the sign tells on which side of the infinite trunk (A219666) it is.

0, -1, 1, 3, -5, -1, 3, 1, 3, -5, -1, 7, -1, -5, -1, -5, 5, 5, -5, -11, 1, 3, -11, 1, -3, 3, 1, 3, -5, -1, 7, -1, -5, -1, -5, 5, 5, -5, -11, 1, 3, -21, 1, -3, -3, 9, 1, -1, -5, -1, -5, 5, 5, -5, -11, 1, 3, -21, 1, -3, -3, -11, -1, -9, -3, 5, 5, -5, -11, 1, 3

Offset

0,4

Comments

Positive and negative terms correspond to the tendrils that sprout respectively at the left and right sides of the infinite trunk, when the factorial beanstalk is drawn with the lesser numbers branching to the left. The absolute values give the sizes of those tendrils, with all nodes included: The leaves, the internal vertices as well as the root itself (which is at A230430(n)).

Here a(0) = 0 is a special case, as the infinite trunk starts to grow from its child 1, while the other child is 0 itself. (For both k=0 or k=1 it is true that A219651(k)=0).

This sequence relates to the factorial base representation (A007623) in the same way as A218618 relates to the binary system.

Links

Antti Karttunen, Table of n, a(n) for n = 0..3149

Formula

a(n) = ((-1)^A230430(n)) * A230427(A230430(n)).

Prog

(Scheme)
(define (A230407 n) (* (expt -1 (A230430 n)) (A230427 (A230430 n))))

Crossrefs

Partial sums: A230408, A230409.

Sequence in context: A005699 A127250 A350882 * A137759 A049246 A231186

Adjacent sequences: A230404 A230405 A230406 * A230408 A230409 A230410

Keyword

sign

Author

Antti Karttunen, Nov 10 2013

Status

approved