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%I #22 Nov 27 2019 07:54:10
%S 1,1,3,6,15,23,53,94,203,404,855,1648,3416,6662,13400,26406,53038,
%T 105306,212051,422162,849267,1696864,3406077,6807024,13642099,
%U 27268122,54576003,109096436,218250874,436243705,872533347,1744312748,3488432736,6974783481
%N Number of compositions of n in which the minimal multiplicity of parts equals 1.
%H Alois P. Heinz and Vaclav Kotesovec, <a href="/A244164/b244164.txt">Table of n, a(n) for n = 1..2000</a> (first 400 terms from Alois P. Heinz)
%H Vaclav Kotesovec, <a href="/A244164/a244164_1.jpg">Graph a(n)/2^n</a>
%F a(n) = 2^(n-1) - A240085(n). - _Gus Wiseman_, Nov 25 2019
%e From _Gus Wiseman_, Nov 25 2019: (Start)
%e The a(1) = 1 through a(5) = 15 compositions:
%e (1) (2) (3) (4) (5)
%e (1,2) (1,3) (1,4)
%e (2,1) (3,1) (2,3)
%e (1,1,2) (3,2)
%e (1,2,1) (4,1)
%e (2,1,1) (1,1,3)
%e (1,2,2)
%e (1,3,1)
%e (2,1,2)
%e (2,2,1)
%e (3,1,1)
%e (1,1,1,2)
%e (1,1,2,1)
%e (1,2,1,1)
%e (2,1,1,1)
%e (End)
%p b:= proc(n, i, p, k) option remember; `if`(n=0, p!, `if`(i<1, 0,
%p add(b(n-i*j, i-1, p+j, k)/j!, j=[0, $max(1, k)..n/i])))
%p end:
%p a:= n-> b(n$2, 0, 1) -b(n$2, 0, 2):
%p seq(a(n), n=1..50);
%t Table[Length[Select[Join@@Permutations/@IntegerPartitions[n],Min@@Length/@Split[Sort[#]]==1&]],{n,0,10}] (* _Gus Wiseman_, Nov 25 2019 *)
%Y Column k=1 of A242451.
%Y The complement is counted by A240085.
%Y Cf. A003242, A098504, A114901, A261983, A329740, A329741.
%K nonn
%O 1,3
%A _Alois P. Heinz_, Jun 21 2014
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