A224342 Apparently solves the identity: find sequence B that represents the numbers of ordered compositions of n using the terms of A, and vice versa.

1, 2, 3, 6, 10, 18, 32, 57, 101, 179, 318, 564, 1002, 1778, 3157, 5604, 9949, 17661, 31352, 55657

Offset: 1

Author

Gary W. Adamson, Apr 03 2013

Keywords

• nonn
• more

Comments

It appears that given any sequence of real numbers taken out of a hat, S(n); repeated iterates of the operation: S(n) -> characteristic function of S(n) -> INVERT transform of the latter -> new sequence, then (repeat), will converge upon two sequences A = A224341 and B = A224342 as a 2-cycle fixed limit.

Alternatively as a conjecture, A and B solve the unique identity as described in the heading as to ordered compositions with A = A224341 and B = A224342. The INVERT transform of the characteristic function of A = B, and the INVERT transform of the characteristic function of B = A.

Examples

			Given the sequence (1, 0, 0, 0, ...) and following the iterative rules, the sequences converge upon A224341 and A224342 as an alternating fixed limit.
		

Crossrefs

Cf. A224341, A079958.

Formula

Repeated trials of any sequence of real numbers pulled out of a hat will apparently converge upon A224341 and A224342 as a 2-cycle fixed limit (absolute values of terms). There is no known generating function at the date of this submission.