positioning 3^k in R-sequence

Fix f to define positions of {3^k}, k being integer, in R-sequence. Function f starts with 1,2,4,7,13,22,38,63 and
is therefore similar to two sequences reported to OEIS: [2] and [3].

To obtain [2], take [1] and create a triangle read by rows: T(n,k) = number of permutations of length n with k inversions
that avoid the “dashed pattern” 1-3 and then take a(n) such that it is the limiting term of the n-th column of the triangle in [1].

Having further calculated the positions of {3^k}:

3 -> 1, 9 -> 2, 27 -> 4
81 -> 7, 243 -> 13, 729 -> 22
2187 -> 38, 6561 -> 63, 19683 -> 102

, we observe that none (neither [2] nor [3]) fit. We have 102 instead of 101 in [3]

To obtain [3] we take numbers of compositions of n into pairwise relatively prime parts. It is also similar to [4], number of peak-avoiding compositions with parts in N, but the difference comes earlier, i.e. after 1, 2, 4, 7, 13, 22, 38.

1. http://oeis.org/A188919
2. http://oeis.org/A188920
3. http://oeis.org/A101268
4. http://oeis.org/A128768

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About misha

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