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.
%I A351722 #45 Apr 09 2022 17:39:37
%S A351722 1,1,1,1,1,9,9,1,1,121,1089,729,729,1521,169,1,1,2601,314721,1771561,
%T A351722 15944049
%N A351722 a(n) is the number of permutations p of {1, 2, ..., 2*n} such that for any k in 1..2*n, k and p(k) do not share a common 1-bit.
%C A351722 By the pigeonhole principle, and simply considering parities of k and p(k), there are no such permutation of {1, 2, ..., 2*n+1}.
%F A351722 a(n) = 1 for any n in A000225 (the only solution is k -> 2*n+1-k).
%F A351722 a(2^k) = 1 for any k >= 0 (the only solution is row 2^k in A253515).
%e A351722 For n = 5:
%e A351722 - we have the following 9 permutations (shown in decimal and in binary):
%e A351722 p\k 1 2 3 4 5 6 7 8 9 10 | 1 10 11 100 101 110 111 1000 1001 1010
%e A351722 --- -----------------------+------------------------------------------------
%e A351722 p1 6 5 4 3 10 9 8 7 2 1 | 110 101 100 11 1010 1001 1000 111 10 1
%e A351722 p2 10 5 4 3 2 9 8 7 6 1 | 1010 101 100 11 10 1001 1000 111 110 1
%e A351722 p3 2 5 4 3 10 9 8 7 6 1 | 10 101 100 11 1010 1001 1000 111 110 1
%e A351722 p4 6 9 4 3 10 1 8 7 2 5 | 110 1001 100 11 1010 1 1000 111 10 101
%e A351722 p5 6 1 4 3 10 9 8 7 2 5 | 110 1 100 11 1010 1001 1000 111 10 101
%e A351722 p6 10 9 4 3 2 1 8 7 6 5 | 1010 1001 100 11 10 1 1000 111 110 101
%e A351722 p7 2 9 4 3 10 1 8 7 6 5 | 10 1001 100 11 1010 1 1000 111 110 101
%e A351722 p8 10 1 4 3 2 9 8 7 6 5 | 1010 1 100 11 10 1001 1000 111 110 101
%e A351722 p9 2 1 4 3 10 9 8 7 6 5 | 10 1 100 11 1010 1001 1000 111 110 101
%e A351722 - so a(5) = 9.
%o A351722 (PARI) a(n) = matpermanent(matrix(2*n, 2*n, i,j, bitand(i,j)==0))
%Y A351722 Cf. A000225, A005326, A109468, A253515, A352857.
%K A351722 nonn,base,more
%O A351722 0,6
%A A351722 _Rémy Sigrist_, Apr 06 2022