A218785 -id:A218785 - cp's OEIS frontend

A218618 Absolute value of a(n) tells the size of the n-th side-tree ("tendril", A213730(n)) in the binary beanstalk; the sign tells on which side of the infinite trunk (A179016) it is.

0, 1, -1, 1, -1, 3, 1, -1, 3, 5, -1, 1, -1, 3, 5, -1, -7, 1, 1, 3, 1, -1, 3, 5, -1, -7, 1, 1, 3, -7, 1, 1, -5, 1, -5, -3, -1, 1, -1, 3, 5, -1, -7, 1, 1, 3, -7, 1, 1, -5, 1, -5, -3, -1, -7, 1, 1, -5, 1, 11, 1, 1, 13, 1, -5, -1, 3, 1, -1, 3, 5, -1, -7, 1, 1, 3

Offset: 0

Antti Karttunen, Dec 03 2012

sign

Positive and negative terms correspond to the tendrils that sprout respectively at the left and right sides of the infinite trunk, when the 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: A213730(n).

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

Partial sums: A218785, A218789. Cf. also A218786, A218613.

(define (A218618 n) (* (expt -1 (A213730 n)) (A213727 (A213730 n))))

a(n) = -1^A213730(n) * A213727(A213730(n)).

A230408 Partial sums of absolute values of A230407.

Original entry on oeis.org

0, 1, 2, 5, 10, 11, 14, 15, 18, 23, 24, 31, 32, 37, 38, 43, 48, 53, 58, 69, 70, 73, 84, 85, 88, 91, 92, 95, 100, 101, 108, 109, 114, 115, 120, 125, 130, 135, 146, 147, 150, 171, 172, 175, 178, 187, 188, 189, 194, 195, 200, 205, 210, 215, 226, 227, 230, 251, 252

Offset: 0

Antti Karttunen, Nov 10 2013

nonn

The term a(n) tells how many nodes there are in total in all side-trees ("tendrils") encountered (see A230430) after we have climbed n steps up along the infinite trunk of the factorial beanstalk, A219666.

This sequence relates to the factorial base representation (A007623) in the same way as A218785 relates to the binary system.

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

Cf. A230407, A230409.

a(0) = 0, a(n) = a(n-1) + |A230407(n)| [Where | | indicates the absolute value].

A255333 Partial sums of A255330.

Original entry on oeis.org

1, 3, 3, 7, 8, 8, 15, 15, 18, 19, 19, 24, 26, 32, 32, 38, 38, 41, 42, 42, 47, 49, 61, 61, 63, 68, 68, 72, 74, 80, 80, 86, 86, 89, 90, 90, 95, 97, 109, 109, 111, 118, 119, 131, 135, 135, 137, 142, 142, 146, 148, 160, 160, 162, 167, 167, 171, 173, 179, 179, 185, 185, 188, 189, 189, 194

Offset: 0

Antti Karttunen, Feb 21 2015

nonn

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

Cf. A000079, A000225, A255061, A255062, A255330, A255332.

Analogous sequences: A218785, A230408.

a(0) = 1; for n >= 1: a(n) = a(n-1) + A255330(n).
Other identities:
a(A255061(n)-1) = A000225(n) - A255062(n) for all n >= 2.
Equally: a(A255061(n)-1) + A255062(n) + 1 = A000079(n) = 2^n for all n >= 2.

cp's OEIS Frontend

A218618 Absolute value of a(n) tells the size of the n-th side-tree ("tendril", A213730(n)) in the binary beanstalk; the sign tells on which side of the infinite trunk (A179016) it is.

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A230408 Partial sums of absolute values of A230407.

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A255333 Partial sums of A255330.

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