A117542
Number of permutations P of 1..n such that in P and in the inverse of P, every pair of adjacent numbers and the first and last number, are relatively prime.
Original entry on oeis.org
1, 2, 6, 8, 36, 16, 127, 320, 581, 1564, 13565, 13760, 149186, 773727, 540538
Offset: 1
a(4)=8, since the 8 permutations (1,2,3,4), (1,4,3,2), (2,1,4,3), (2,3,4,1), (4,1,2,3), (3,2,1,4), (3,4,1,2), (4,3,2,1) satisfy the property.
A168078
Number of matrices with elements 1..n in which every pair of adjacent elements are relatively prime.
Original entry on oeis.org
1, 4, 12, 32, 144, 176, 1728, 4320, 27936
Offset: 1
A116542
Table B(m,n), read by antidiagonals, where B(m,n) is the number of ways integers 1,..,m*n can be put into an m X n grid so that every adjacent (NESW) pair of integers are coprime.
Original entry on oeis.org
1, 2, 2, 6, 8, 6, 12, 16, 16, 12, 72, 432, 2016, 432, 72, 72, 2784, 23904, 23904, 2784, 72, 864, 35712, 7102656, 19611648, 7102656, 35712, 864
Offset: 1
The 16 configuration 3x2 are the following
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1 2 3 | 2 5 6 | 3 4 1 | 4 5 6 | 6 1 2 | 6 5 4
6 5 4 | 3 4 1 | 2 5 6 | 3 2 1 | 5 4 3 | 1 2 3
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1 4 3 | 3 2 1 | 3 4 5 | 5 2 3 | 6 1 4
6 5 2 | 4 5 6 | 2 1 6 | 6 1 4 | 5 2 3
------------------------------------------------
2 1 6 | 3 2 5 | 4 1 6 | 5 4 3 | 6 5 2
3 4 5 | 4 1 6 | 3 2 5 | 6 1 2 | 1 4 3
------------------------------------------------
A369330
Number of permutations of (1, 2, ..., n) in which any two adjacent elements differ by a power of 2.
Original entry on oeis.org
1, 1, 2, 6, 12, 48, 140, 338, 926, 4390, 15990, 52766, 187688, 557768, 1772354, 5865806, 18707354, 102862912, 456146172, 1833942698, 7914142056, 30247599368, 120022505534, 492976337746, 1992746442918, 7203060422116, 27454886930170, 106007544478780, 398728610528654
Offset: 0
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