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Number of 4-shaft weaving patterns, threaded 1,2,3,4, with n rows, up to symmetries.
0

%I #70 Feb 05 2023 11:52:46

%S 0,3,30,465,5591,71722,893120,11228834,141465194

%N Number of 4-shaft weaving patterns, threaded 1,2,3,4, with n rows, up to symmetries.

%C This is the number of n X 4 arrays with entries in {0,1} such that

%C (a) every row and every column contains at least one 0

%C (b) every row and every column contains at least one 1

%C where two arrays that can be transformed into each other by

%C any composition of the four operations below are considered equivalent.

%C (1) rotate all the rows by some fixed amount

%C (2) rotate all the columns by some fixed amount

%C (3) reverse the order of all rows

%C (4) reverse the order of all columns.

%C 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.

%e 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]].

%K nonn,more

%O 1,2

%A _Jeffrey Shallit_, Jan 22 2023

%E a(7)-a(9) from _Bert Dobbelaere_, Feb 05 2023