A261099 - OEIS

%I #10 Sep 24 2015 01:40:35

%S 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,

%T 48,48,60,64,71,67,86,93,74,94,74,85,116,111,119,99,108,99,30,30,86,

%U 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

%N Main diagonal of A261096.

%C Equally: main diagonal of A261097.

%C 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.

%H Antti Karttunen, <a href="/A261099/b261099.txt">Table of n, a(n) for n = 0..5040</a>

%F a(n) = A261096(n,n) = A261097(n,n).

%F By conjugating a similar sequence:

%F a(n) = A060119(A261219(A060126(n))).

%Y Main diagonal of A261096 and A261097.

%Y Cf. A014489 (the positions of zeros).

%Y Cf. A055089, A195663.

%Y Cf. also A261219.

%Y Related permutations: A060119, A060126.

%K nonn

%O 0,4

%A _Antti Karttunen_, Aug 26 2015