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%I #16 Mar 03 2021 21:51:04
%S 1,1,3,7,16,34,73,155,324,674,1393,2861,5852,11929,24239,49127,99360,
%T 200598,404377,814135,1637363,3290067,6605980,13255451,26583994,
%U 53290694,106787166,213919062,428415074,857794856,1717201360,3437092882,6878672565,13764822699
%N The sum of the sizes of the largest fixed points over all compositions of n.
%D M. Archibald, A. Blecher and A. Knopfmacher, Fixed points in compositions and words, accepted by the Journal of Integer Sequences.
%H Alois P. Heinz, <a href="/A335713/b335713.txt">Table of n, a(n) for n = 1..500</a>
%H M. Archibald, A. Blecher, and A. Knopfmacher, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL23/Blecher/arch14.html">Fixed Points in Compositions and Words</a>, J. Int. Seq., Vol. 23 (2020), Article 20.11.1.
%F G.f.: Sum_{j>=1} (x/(1-x))^(j-1) j x^j Sum_{k>=j} Product_{i=j+1..k} (x/(1-x) - x^i).
%e For n=3 the a(3)=3 values are the first 1 in the composition 111 and the 2 in the composition 12 (the compositions 21 and 3 do not have any fixed points).
%Y Cf. A099036, A335712, A335714.
%K nonn
%O 1,3
%A _Margaret Archibald_, Jun 18 2020
%E a(21)-a(34) from _Alois P. Heinz_, Jun 18 2020
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