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A329768 Number of finite sequences of positive integers whose sum minus runs-resistance is n.

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%I A329768 #4 Nov 22 2019 16:13:34
%S A329768 8,17,42,104,242,541,1212,2664,5731,12314
%N A329768 Number of finite sequences of positive integers whose sum minus runs-resistance is n.
%C A329768 A composition of n is a finite sequence of positive integers with sum n.
%C A329768 For the operation of taking the sequence of run-lengths of a finite sequence, runs-resistance is defined as the number of applications required to reach a singleton.
%H A329768 Claude Lenormand, <a href="/A318921/a318921.pdf">Deux transformations sur les mots</a>, Preprint, 5 pages, Nov 17 2003.
%e A329768 The a(1) = 8 and a(2) = 17 compositions whose sum minus runs-resistance is n:
%e A329768   (1)        (2)
%e A329768   (1,1)      (1,3)
%e A329768   (1,2)      (3,1)
%e A329768   (2,1)      (1,1,1)
%e A329768   (1,1,2)    (1,1,3)
%e A329768   (2,1,1)    (1,2,1)
%e A329768   (1,1,2,1)  (1,2,2)
%e A329768   (1,2,1,1)  (2,2,1)
%e A329768              (3,1,1)
%e A329768              (1,1,1,2)
%e A329768              (1,1,3,1)
%e A329768              (1,3,1,1)
%e A329768              (2,1,1,1)
%e A329768              (1,1,1,2,1)
%e A329768              (1,2,1,1,1)
%e A329768              (1,2,1,1,2)
%e A329768              (2,1,1,2,1)
%Y A329768 Column sums of A329750.
%Y A329768 Cf. A000740, A008965, A098504, A242882, A318928, A329744, A329745, A329746, A329747, A329767.
%K A329768 nonn,more
%O A329768 1,1
%A A329768 _Gus Wiseman_, Nov 21 2019