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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.

%I A089839 #5 Mar 31 2012 14:02:17
%S A089839 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,
%T A089839 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,
%U A089839 10,17,1655095,1654694,0,0,0,1654694,1654255,16,10
%N 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.
%C A089839 This is a "multiplication table" of an infinite enumerable group. Each row and column is a permutation of A001477.
%H A089839 A. Karttunen, <a href="/A089839/a089839.c.txt">C-program for computing the elements of this table</a>
%e A089839 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".
%Y A089839 Column 1: A089837, row 1: A089838, the main diagonal: A089841.
%K A089839 nonn,tabl
%O A089839 0,4
%A A089839 _Antti Karttunen_, Dec 05 2003