A218618 -id:A218618 - cp's OEIS frontend

A218789 Partial sums of A218618.

0, 1, 0, 1, 0, 3, 4, 3, 6, 11, 10, 11, 10, 13, 18, 17, 10, 11, 12, 15, 16, 15, 18, 23, 22, 15, 16, 17, 20, 13, 14, 15, 10, 11, 6, 3, 2, 3, 2, 5, 10, 9, 2, 3, 4, 7, 0, 1, 2, -3, -2, -7, -10, -11, -18, -17, -16, -21, -20, -9, -8, -7, 6, 7, 2, 1, 4, 5, 4, 7, 12

Offset: 0

Antti Karttunen, Dec 03 2012

The term a(n) indicates approximately the "balance" of the binary beanstalk (cf. A179016) at n steps up from the root, which in turn has repercussions for the sequences such as A218542 and A218543.

Antti Karttunen, Table of n, a(n) for n = 0..30901

Cf. A179016, A218618, A218603, A218604, A218543.

A218785 Partial sums of absolute values of A218618.

Original entry on oeis.org

0, 1, 2, 3, 4, 7, 8, 9, 12, 17, 18, 19, 20, 23, 28, 29, 36, 37, 38, 41, 42, 43, 46, 51, 52, 59, 60, 61, 64, 71, 72, 73, 78, 79, 84, 87, 88, 89, 90, 93, 98, 99, 106, 107, 108, 111, 118, 119, 120, 125, 126, 131, 134, 135, 142, 143, 144, 149, 150, 161, 162, 163

Offset: 0

Antti Karttunen, Dec 03 2012

nonn

The term a(n) tells how many nodes there are in total in all side-trees ("tendrils") encountered (see A213730) after we have walked n steps up along the infinite stem of the binary beanstalk, A179016.

Antti Karttunen, Table of n, a(n) for n = 0..8727

Cf. A218789.

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.

Original entry on oeis.org

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

Antti Karttunen, Nov 10 2013

sign

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.

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

Partial sums: A230408, A230409.

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

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

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A218789 Partial sums of A218618.

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A218785 Partial sums of absolute values of A218618.

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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.

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