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%I #9 Feb 20 2022 15:11:45
%S 1,2,4,7,13,25,46,86,161,301,562,1051,1964,3670,6859,12819,23956,
%T 44772,83673
%N 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.
%C 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.
%C 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.
%F The sequences are obtained by taking iterates as described in the comments. There is no known generating function at the date of this submission.
%e Given the sequence (1, 0, 0, 0, ...), a few iterates using the rules rapidly converge upon A224341 and A224342.
%Y Cf. A224342, A079958.
%K nonn
%O 0,2
%A _Gary W. Adamson_, Apr 03 2013
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