cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A174076 Number of permutations of length n with no consecutive triples i,i+2,i+4 or i,i-2,i-4.

Original entry on oeis.org

1, 1, 2, 6, 24, 108, 632, 4408, 35336, 319056, 3205824, 35451984, 427683560, 5588310904, 78615281768, 1184587864512, 19033796498496, 324852522308160, 5868833343451592, 111889157407344424
Offset: 0

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Author

Isaac Lambert, Mar 10 2010

Keywords

Comments

Note for n<5 there are no such subsequences, so those values are trivially n!. Also note it is possible for a permutation to have both i,i+2,i+4 and i,i-2,i-4 triples, as in an example from n=7: (2,4,6,5,3,1,0). This permutation is not counted by a(7).

Examples

			For n=5 there are 5!-a(5)=12 permutations with i,i+2,i+4 or i,i-2,i-4 triples. An examples of one is (4,2,0,1,3).
		

Crossrefs

Extensions

a(0)-a(4) and a(10)-a(19) from Alois P. Heinz, Apr 14 2021

A174078 Number of circular permutations of length n with no consecutive triples i,i+2,i+4 or i,i-2,i-4.

Original entry on oeis.org

20, 100, 600, 4244, 34264, 311424, 3143912, 34833964, 420917638, 5513592091, 77715460917
Offset: 5

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Author

Isaac Lambert, Mar 10 2010

Keywords

Comments

Circular permutations are permutations whose indices are from the ring of integers modulo n.

Examples

			For n=5 there are (5-1)!-a(5)=4 circular permutations with i,i+2,i+4 or i,i-2,i-4 triples. They are (0,2,4,1,3), (0,2,4,3,1), (0,1,3,4,2), and (0,3,1,4,2).
		

Crossrefs

Extensions

a(10)-a(15) from Donovan Johnson, Sep 24 2010

A174079 Number of circular permutations of length n with no consecutive triples i,i+2,i+4 (mod n) or i,i-2,i-4 (mod n).

Original entry on oeis.org

12, 84, 494, 3696, 30574
Offset: 5

Views

Author

Isaac Lambert, Mar 10 2010

Keywords

Comments

Circular permutations are permutations whose indices are from the ring of integers modulo n.

Examples

			For n=5 there are (5-1)!-a(5)=12 circular permutations with triples i,i+2,i+4 (mod 5) or triples i,i-2,i-4 (mod 5). An example of one is (0,3,1,2,4) because of the progression 0,3,1 (mod 5).
		

Crossrefs

Showing 1-3 of 3 results.