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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. 2
1, 2, 3, 6, 10, 18, 32, 57, 101, 179, 318, 564, 1002, 1778, 3157, 5604, 9949, 17661, 31352, 55657 (list; graph; refs; listen; history; text; internal format)



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.


Table of n, a(n) for n=1..20.


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.


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


Cf. A224341, A079958.

Sequence in context: A147852 A061279 A018073 * A181649 A052972 A018166

Adjacent sequences:  A224339 A224340 A224341 * A224343 A224344 A224345




Gary W. Adamson, Apr 03 2013



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Last modified September 22 14:32 EDT 2021. Contains 347607 sequences. (Running on oeis4.)