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%I #9 Sep 24 2015 01:41:20
%S 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,
%T 54,54,60,65,66,69,84,90,78,95,84,81,114,108,114,107,102,111,0,0,74,
%U 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
%N Main diagonal of A261216: a(n) = A261216(n,n).
%C Equally: main diagonal of A261217.
%C 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.
%H Antti Karttunen, <a href="/A261219/b261219.txt">Table of n, a(n) for n = 0..5040</a>
%F a(n) = A261216(n,n) = A261217(n,n).
%F By conjugating a similar sequence:
%F a(n) = A060126(A261099(A060119(n))).
%Y Main diagonal of A261216 and A261217.
%Y Cf. A261220 (the positions of zeros).
%Y Cf. A060117, A060118.
%Y Cf. also A261099, A089841.
%Y Related permutations: A060119, A060126.
%K nonn
%O 0,4
%A _Antti Karttunen_, Aug 26 2015
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