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A359972
Number of 4-shaft weaving patterns, threaded 1,2,3,4, with n rows, up to symmetries.
0
0, 3, 30, 465, 5591, 71722, 893120, 11228834, 141465194
OFFSET
1,2
COMMENTS
This is the number of n X 4 arrays with entries in {0,1} such that
(a) every row and every column contains at least one 0
(b) every row and every column contains at least one 1
where two arrays that can be transformed into each other by
any composition of the four operations below are considered equivalent.
(1) rotate all the rows by some fixed amount
(2) rotate all the columns by some fixed amount
(3) reverse the order of all rows
(4) reverse the order of all columns.
The motivation is that two arrays A and B are considered equivalent if tiling the plane with translated copies of A (resp., B) results in essentially the same pattern.
EXAMPLE
For n = 2 the 3 patterns are [[0,0,0,1],[1,1,1,0]], [[0,0,1,1],[1,1,0,0]], and [[0,1,0,1],[1,0,1,0]].
CROSSREFS
Sequence in context: A354287 A276361 A360973 * A218304 A242005 A276356
KEYWORD
nonn,more
AUTHOR
Jeffrey Shallit, Jan 22 2023
EXTENSIONS
a(7)-a(9) from Bert Dobbelaere, Feb 05 2023
STATUS
approved