%I #11 Apr 30 2019 08:26:12

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

%T 31352,55657

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

%C 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.

%C 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.

%F 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.

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

%Y Cf. A224341, A079958.

%K nonn,more

%O 1,2

%A _Gary W. Adamson_, Apr 03 2013