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A383212 a(n) = permanent of the n-th principal submatrix of the rectangular array whose odd-numbered rows are (2,1,2,1,2,1,2,1,...) and even-numbered rows are (1,2,1,2,1,2,1,2,...).

%I A383212 #18 Apr 24 2025 09:01:55
%S A383212 1,2,5,24,132,1032,8820,95616,1106496,15327360,223560000,3768768000,
%T A383212 66305952000,1316927808000,27127003680000,620221722624000,
%U A383212 14638710417408000,378633583448064000,10073602372700160000,290788929384726528000,8609476463579013120000,274361332654900592640000,8946658680536444313600000
%N A383212 a(n) = permanent of the n-th principal submatrix of the rectangular array whose odd-numbered rows are (2,1,2,1,2,1,2,1,...) and even-numbered rows are (1,2,1,2,1,2,1,2,...).
%p A383212 1, seq(LinearAlgebra:-Permanent(Matrix(n,n,(i,j) -> 1 + (i+j+1 mod 2))), n=1..22); # _Robert Israel_, Apr 23 2025
%t A383212 a[i_, j_] := If[EvenQ[i + j], 2, 1];
%t A383212 m[n_] := Table[a[i, j], {i, 1, n}, {j, 1, n}];
%t A383212 Join[{1}, Table[Permanent[m[n]], {n, 1, 19}]]
%o A383212 (PARI) a(n) = {matpermanent(matrix(n, n, i, j, 2 - (i+j)%2))};
%o A383212 for(n=0, 25, print1(a(n), ", ")) \\ _Vaclav Kotesovec_, Apr 21 2025
%Y A383212 Cf. A204252.
%K A383212 nonn
%O A383212 0,2
%A A383212 _Clark Kimberling_, Apr 19 2025
%E A383212 a(20)-a(22) from _Vaclav Kotesovec_, Apr 21 2025