A261219 - OEIS

A261219

Main diagonal of A261216: a(n) = A261216(n,n).

0, 0, 0, 5, 0, 3, 0, 0, 14, 16, 22, 20, 0, 19, 8, 20, 0, 7, 0, 13, 0, 7, 10, 16, 0, 0, 0, 5, 0, 3, 54, 54, 60, 65, 66, 69, 84, 90, 78, 95, 84, 81, 114, 108, 114, 107, 102, 111, 0, 0, 74, 76, 100, 98, 30, 30, 78, 83, 102, 105, 0, 19, 26, 45, 100, 119, 0, 13, 74, 87, 28, 41, 0, 97, 50, 98, 0, 49, 0, 97, 26, 117, 22, 47, 36, 108, 60, 113, 36, 63, 0, 25, 50, 33, 10, 59, 0, 73, 0, 49, 52

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OFFSET

0,4

COMMENTS

Equally: main diagonal of A261217.

For permutation p, which has rank n in permutation list A060117, 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. Equally, if permutation p has rank n in the order used in list A060118, a(n) gives the rank of the p*p in that same list. Thus zeros (which mark the identity permutation, with rank 0 in both orders) occur at positions where the permutations of A060117 (equally: of A060118) are involutions, listed by A261220.

LINKS

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

FORMULA

a(n) = A261216(n,n) = A261217(n,n).

By conjugating a similar sequence:

a(n) = A060126(A261099(A060119(n))).

CROSSREFS

Main diagonal of A261216 and A261217.

Cf. A261220 (the positions of zeros).

Cf. A060117, A060118.

Cf. also A261099, A089841.

Related permutations: A060119, A060126.