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

A174077 Number of 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

1, 1, 2, 0, 24, 80, 504, 3794, 31616, 290970, 2973600, 33311520, 405781344, 5342413414, 75612197528, 1144942063230, 18471128518656, 316309310084728, 5730646943736936
Offset: 0

Views

Author

Isaac Lambert, Mar 10 2010

Keywords

Examples

			As an example, (0,4,1,2,3) is counted by a(5), but (0,4,1,3,2) is not because it has the progression 4,1,3.
		

Crossrefs

Extensions

Definition corrected by Isaac Lambert, Mar 15 2010
a(0)-a(4) and a(10)-a(18) from Alois P. Heinz, Apr 15 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

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)=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
Showing 1-3 of 3 results.