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A204252 Permanent of the n-th principal submatrix of A201208 (in square format).

%I A204252 #22 Apr 23 2025 17:54:31
%S A204252 1,5,18,132,876,8820,85392,1106496,14057280,223560000,3513456000,
%T A204252 66305952000,1241430624000,27127003680000,589395356928000,
%U A204252 14638710417408000,362021985626112000,10073602372700160000,279369787588448256000,8609476463579013120000,264609942011693752320000
%N A204252 Permanent of the n-th principal submatrix of A201208 (in square format).
%H A204252 Vaclav Kotesovec, <a href="/A204252/b204252.txt">Table of n, a(n) for n = 1..30</a>
%p A204252 a:= n-> LinearAlgebra[Permanent](Matrix(n, (i, j)-> 1+irem(i+j, 2))):
%p A204252 seq(a(n), n=1..20);  # _Alois P. Heinz_, Apr 23 2025
%t A204252 f[i_, j_] := 1 + Mod[i + j, 2];
%t A204252 m[n_] := Table[f[i, j], {i, 1, n}, {j, 1, n}]
%t A204252 TableForm[m[8]] (* 8x8 principal submatrix *)
%t A204252 Flatten[Table[f[i, n + 1 - i],
%t A204252   {n, 1, 12}, {i, 1, n}]] (* A201208 in square format *)
%t A204252 Permanent[m_] :=
%t A204252   With[{a = Array[x, Length[m]]},
%t A204252    Coefficient[Times @@ (m.a), Times @@ a]];
%t A204252 Table[Permanent[m[n]], {n, 1, 20}]    (* A204252 *)
%o A204252 (PARI) a(n) = {matpermanent(matrix(n, n, i, j, 1 + (i+j)%2))};
%o A204252 for(n=1, 25, print1(a(n), ", ")) \\ _Vaclav Kotesovec_, Apr 21 2025
%Y A204252 Cf. A201208, A383212.
%K A204252 nonn
%O A204252 1,2
%A A204252 _Clark Kimberling_, Jan 14 2012
%E A204252 a(20)-a(21) from _Pontus von Brömssen_, Mar 03 2024