A014489 -id:A014489 - cp's OEIS frontend

A261220 Ranks of involutions in permutation orderings A060117 and A060118.

0, 1, 2, 4, 6, 7, 12, 16, 18, 20, 24, 25, 26, 28, 48, 49, 60, 66, 72, 76, 78, 90, 96, 98, 102, 108, 120, 121, 122, 124, 126, 127, 132, 136, 138, 140, 240, 241, 242, 244, 288, 289, 312, 316, 336, 338, 360, 361, 372, 378, 384, 385, 432, 450, 456, 468, 480, 484, 486, 498, 504, 508, 528, 546, 576, 582, 600, 602, 606, 612, 624, 626, 648, 660, 672, 678, 720, 721

Offset: 0

Antti Karttunen, Aug 26 2015

From Antti Karttunen, Aug 17 2016: (Start)
Intersection of A275804 and A276005. In other words, these are numbers in whose factorial base representation (A007623, see A260743) there does not exist any such pair of nonzero digits d_i and d_j in positions i and j that either (i - d_i) = j or (i - d_i) = (j - d_j) would hold. Here one-based indexing is used so that the least significant digit at right is in position 1.
(End)

Antti Karttunen, Table of n, a(n) for n = 0..1000
Index entries for sequences related to factorial base representation

Intersection of A275804 and A276005.
Same sequence shown in factorial base: A260743.
Cf. A060117, A060118, A275947, A276007.
Positions of zeros in A261219.
Positions of 1 and 2's in A060131 and A275803.
Subsequence: A060112.
Cf. also A014489.

A261099 Main diagonal of A261096.

Original entry on oeis.org

0, 0, 0, 4, 3, 0, 0, 0, 12, 16, 23, 19, 8, 23, 0, 20, 0, 7, 16, 11, 15, 0, 7, 0, 0, 0, 0, 4, 3, 0, 48, 48, 60, 64, 71, 67, 86, 93, 74, 94, 74, 85, 116, 111, 119, 99, 108, 99, 30, 30, 86, 89, 112, 111, 0, 0, 78, 82, 107, 103, 0, 20, 26, 46, 96, 103, 15, 0, 41, 29, 78, 73, 60, 115, 38, 119, 38, 63, 56, 107, 0, 104, 0, 55, 26, 100, 0, 104, 19, 42, 33, 56, 11, 52, 0, 25

Offset: 0

Antti Karttunen, Aug 26 2015

nonn

Equally: main diagonal of A261097.

For permutation p, which has rank n in permutation list A055089 (A195663), a(n) gives the rank of the "square" of that permutation (obtained by composing it with itself as: q(i) = p(p(i))) in the same list. Thus zeros (which mark the identity permutation, with rank 0) occur at positions where the permutations of A055089/A195663 are involutions, listed by A014489.

Antti Karttunen, Table of n, a(n) for n = 0..5040

Main diagonal of A261096 and A261097.
Cf. A014489 (the positions of zeros).
Cf. A055089, A195663.
Cf. also A261219.
Related permutations: A060119, A060126.

a(n) = A261096(n,n) = A261097(n,n).
By conjugating a similar sequence:
a(n) = A060119(A261219(A060126(n))).

cp's OEIS Frontend

A261220 Ranks of involutions in permutation orderings A060117 and A060118.

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