[seqfan] A178841 and A152537 are almost the same - why?

[Georg.Fischer]

Hi Seqfans,

the 1000 terms in the b-files of

A178841 The number of pure inverting compositions of n.
         nonn,more,changed, Aaron Lauve (lauve(AT)math.luc.edu),
         Jun 17 2010
A152537 Convolution sequence: convolved with A000041 =
         powers of 2, (A000079).
         nonn, _Gary W. Adamson_, Dec 06 2008

are almost the same, though the sequences do not refer
to each other. The differences occur in rare pairs (with
increasing distance) where A178841(n + 1) = A152537(n) + 1.

You see them in the lines with vertical bars in
<http://teherba.org/OEIS-mat/coincidence/work/1543.diff.txt>

Maybe the coincidence (and the difference) is easy to
explain, but I cannot.

BTW, the "more" keyword of A178841 might be removed.

Best regards - Georg