cp's OEIS Frontend

A335455 Number of compositions of n with some part appearing more than twice.

%I A335455 #10 Jun 30 2020 09:54:08
%S A335455 0,0,0,1,1,5,11,30,69,142,334,740,1526,3273,6840,14251,29029,59729,
%T A335455 122009,248070,500649,1012570,2040238,4107008,8257466,16562283,
%U A335455 33229788,66621205,133478437,267326999,535146239,1071183438,2143604313,4289194948,8581463248
%N A335455 Number of compositions of n with some part appearing more than twice.
%C A335455 Also the number of compositions of n matching the pattern (1,1,1).
%C A335455 A composition of n is a finite sequence of positive integers summing to n.
%H A335455 Wikipedia, <a href="https://en.wikipedia.org/wiki/Permutation_pattern">Permutation pattern</a>
%H A335455 Gus Wiseman, <a href="https://oeis.org/A102726/a102726.txt">Sequences counting and ranking compositions by the patterns they match or avoid.</a>
%F A335455 a(n > 0) = 2^(n - 1) - A232432(n).
%e A335455 The a(3) = 1 through a(6) = 11 compositions:
%e A335455   (111)  (1111)  (1112)   (222)
%e A335455                  (1121)   (1113)
%e A335455                  (1211)   (1131)
%e A335455                  (2111)   (1311)
%e A335455                  (11111)  (3111)
%e A335455                           (11112)
%e A335455                           (11121)
%e A335455                           (11211)
%e A335455                           (12111)
%e A335455                           (21111)
%e A335455                           (111111)
%t A335455 Table[Length[Select[Join@@Permutations/@IntegerPartitions[n],Max@@Length/@Split[Sort[#]]>=3&]],{n,0,10}]
%Y A335455 The case of partitions is A000726.
%Y A335455 The avoiding version is A232432.
%Y A335455 The (1,1)-matching version is A261982.
%Y A335455 The version for patterns is A335508.
%Y A335455 The version for prime indices is A335510.
%Y A335455 These compositions are ranked by A335512.
%Y A335455 Compositions are counted by A011782.
%Y A335455 Combinatory separations are counted by A269134.
%Y A335455 Normal patterns matched by compositions are counted by A335456.
%Y A335455 Cf. A000740, A034691, A056986, A080599, A106356, A181796, A232464, A238279, A333755.
%K A335455 nonn
%O A335455 0,6
%A A335455 _Gus Wiseman_, Jun 15 2020