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A335511
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Number of (1,1,1)-avoiding permutations of the prime indices of n.
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6
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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, 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, 2, 6, 1, 0, 1, 2, 3, 3, 2, 6, 1, 0, 0, 2, 1, 12, 2, 2
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OFFSET
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1,6
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COMMENTS
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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).
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LINKS
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FORMULA
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If n is cubefree, a(n) = A008480(n), otherwise a(n) = 0.
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MATHEMATICA
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primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Table[Length[Select[Permutations[primeMS[n]], !MatchQ[#, {___, x_, ___, x_, ___, x_, ___}]&]], {n, 100}]
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CROSSREFS
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Patterns avoiding this pattern are counted by A080599.
These compositions are counted by A232432.
The (1,1)-avoiding version is A335451.
The complement A335510 is the matching version.
These permutations are ranked by A335513.
Permutations of prime indices are counted by A008480.
Anti-run permutations of prime indices are counted by A335452.
Cf. A056239, A056986, A112798, A238279, A281188, A333221, A333755, A335456, A335460, A335462, A335463.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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