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

Author

Gary W. Adamson, Apr 03 2013

Keywords

• nonn

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.

Examples

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

Crossrefs

Cf. A224342, A079958.

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.