A224341 Apparently solves the identity: Find sequence A that represents the numbers of ordered compositions of n into the elements of the set {B}; and vice versa.

1, 2, 4, 7, 13, 25, 46, 86, 161, 301, 562, 1051, 1964, 3670, 6859, 12819, 23956, 44772, 83673

Offset

0,2

Comments

Represents the numbers of ordered compositions of n using the terms of A224342: (1, 2, 3, 6, 10, 18, 32, ...); such that the latter represents the numbers of ordered compositions of n using the terms of A224341.

It appears that given any sequence of real terms pulled out of a hat S(n); repeated iterates of S(n) -> characteristic function of S(n) -> INVERT transform of the latter -> next sequence, (repeat); will converge upon two alternating sequences A224341 and A224342 as a fixed limit, as to absolute values.

Links

Table of n, a(n) for n=0..18.

Formula

The sequences are obtained by taking iterates as described in the comments. There is no known generating function at the date of this submission.

Example

Given the sequence (1, 0, 0, 0, ...), a few iterates using the rules rapidly converge upon A224341 and A224342.

Crossrefs

Cf. A224342, A079958.

Sequence in context: A358334 A000074 A079958 * A235684 A367400 A018082

Adjacent sequences: A224338 A224339 A224340 * A224342 A224343 A224344

Keyword

nonn

Author

Gary W. Adamson, Apr 03 2013

Status

approved