cp's OEIS Frontend

A335511 Number of (1,1,1)-avoiding permutations of the prime indices of n.

%I A335511 #8 Jun 30 2020 09:56:00
%S A335511 1,1,1,1,1,2,1,0,1,2,1,3,1,2,2,0,1,3,1,3,2,2,1,0,1,2,0,3,1,6,1,0,2,2,
%T A335511 2,6,1,2,2,0,1,6,1,3,3,2,1,0,1,3,2,3,1,0,2,0,2,2,1,12,1,2,3,0,2,6,1,3,
%U A335511 2,6,1,0,1,2,3,3,2,6,1,0,0,2,1,12,2,2
%N A335511 Number of (1,1,1)-avoiding permutations of the prime indices of n.
%C A335511 We define a pattern to be a finite sequence covering an initial interval of positive integers. Patterns are counted by A000670 and ranked by A333217. A sequence S is said to match a pattern P if there is a not necessarily contiguous subsequence of S whose parts have the same relative order as P. For example, (3,1,1,3) matches (1,1,2), (2,1,1), and (2,1,2), but avoids (1,2,1), (1,2,2), and (2,2,1).
%H A335511 Wikipedia, <a href="https://en.wikipedia.org/wiki/Permutation_pattern">Permutation pattern</a>
%H A335511 Gus Wiseman, <a href="https://oeis.org/A102726/a102726.txt">Sequences counting and ranking compositions by the patterns they match or avoid.</a>
%F A335511 If n is cubefree, a(n) = A008480(n), otherwise a(n) = 0.
%t A335511 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A335511 Table[Length[Select[Permutations[primeMS[n]],!MatchQ[#,{___,x_,___,x_,___,x_,___}]&]],{n,100}]
%Y A335511 Patterns avoiding this pattern are counted by A080599.
%Y A335511 These compositions are counted by A232432.
%Y A335511 The (1,1)-avoiding version is A335451.
%Y A335511 The complement A335510 is the matching version.
%Y A335511 These permutations are ranked by A335513.
%Y A335511 Patterns are counted by A000670 and ranked by A333217.
%Y A335511 Permutations of prime indices are counted by A008480.
%Y A335511 Anti-run permutations of prime indices are counted by A335452.
%Y A335511 Cf. A056239, A056986, A112798, A238279, A281188, A333221, A333755, A335456, A335460, A335462, A335463.
%K A335511 nonn
%O A335511 1,6
%A A335511 _Gus Wiseman_, Jun 19 2020