A089841 -id:A089841 - cp's OEIS frontend

A089839 Array A(x,y): (read as A(0,0), A(1,0), A(0,1), A(2,0), A(1,1), A(0,2), A(3,0), A(2,1), A(1,2), A(0,3),...) Position of the composition A089840[y] o A089840[x] in the table A089840.

0, 1, 1, 2, 0, 2, 3, 14, 19, 3, 4, 15, 0, 21, 4, 5, 16, 6, 4, 17, 5, 6, 13, 5, 0, 3, 18, 6, 7, 12, 4, 2, 5, 6, 20, 7, 8, 21, 3, 6, 6, 4, 5, 15, 8, 9, 18, 1654606, 5, 2, 3, 2, 1654137, 13, 9, 10, 17, 1655095, 1654694, 0, 0, 0, 1654694, 1654255, 16, 10

Offset: 0

Antti Karttunen, Dec 05 2003

This is a "multiplication table" of an infinite enumerable group. Each row and column is a permutation of A001477.

			A(2,1)=14 because A089840[2] = A072796, A089840[1] = A069770 and the composition A069770 o A072796 (here the right hand side permutation acts first) yields A073269 = A089840[14]. Similarly A(2,2)=0, as A089840[2] = A072796, which being an involution, yields A001477 (= A089840[0]) when "squared".

A. Karttunen, C-program for computing the elements of this table

Column 1: A089837, row 1: A089838, the main diagonal: A089841.

A261219 Main diagonal of A261216: a(n) = A261216(n,n).

Original entry on oeis.org

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

Offset: 0

Antti Karttunen, Aug 26 2015

nonn

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.

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

Main diagonal of A261216 and A261217.
Cf. A261220 (the positions of zeros).
Cf. A060117, A060118.
Cf. also A261099, A089841.
Related permutations: A060119, A060126.

a(n) = A261216(n,n) = A261217(n,n).
By conjugating a similar sequence:
a(n) = A060126(A261099(A060119(n))).

cp's OEIS Frontend

A089839 Array A(x,y): (read as A(0,0), A(1,0), A(0,1), A(2,0), A(1,1), A(0,2), A(3,0), A(2,1), A(1,2), A(0,3),...) Position of the composition A089840[y] o A089840[x] in the table A089840.

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