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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.
2
1, 2, 4, 7, 13, 25, 46, 86, 161, 301, 562, 1051, 1964, 3670, 6859, 12819, 23956, 44772, 83673
OFFSET
0,2
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.
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.
EXAMPLE
Given the sequence (1, 0, 0, 0, ...), a few iterates using the rules rapidly converge upon A224341 and A224342.
CROSSREFS
Sequence in context: A000074 A374517 A079958 * A235684 A367400 A018082
KEYWORD
nonn
AUTHOR
Gary W. Adamson, Apr 03 2013
STATUS
approved