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%I #20 Mar 03 2021 21:50:56
%S 1,1,2,6,12,27,54,115,237,486,997,2030,4122,8350,16881,34054,68609,
%T 138052,277500,557328,1118546,2243589,4498004,9014053,18058159,
%U 36166338,72415886,144970116,290170091,580721926,1162077483,2325206168,4652155420,9307199819
%N The sum of the sizes of the minimal 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="/A335712/b335712.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} (Product_{i=1..j-1} (x/(1-x)-x^i)) j x^j (1-x)/(1-2x).
%e Example: For n=3 the a(3)=2 values are the first 1s in 111 and 12 (the other compositions 21 and 3 do not have any fixed points).
%o (PARI) my(N=44,x='x+O('x^N)); Vec( sum(j=1, N, prod(i=1, j-1, (x/(1-x)-x^i) ) *j*x^j * (1-x)/(1-2*x) ) ) \\ _Joerg Arndt_, Jun 18 2020
%Y Cf. A099036, A335713, 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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