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A204240 Determinant of the n-th principal submatrix of A204158.

%I A204240 #12 Feb 21 2015 11:48:57
%S A204240 1,-14,115,-800,5125,-31250,184375,-1062500,6015625,-33593750,
%T A204240 185546875,-1015625000,5517578125,-29785156250,159912109375,
%U A204240 -854492187500,4547119140625,-24108886718750,127410888671875,-671386718750000
%N A204240 Determinant of the n-th principal submatrix of A204158.
%H A204240 Colin Barker, <a href="/A204240/b204240.txt">Table of n, a(n) for n = 1..100</a>
%F A204240 Conjectures from _Colin Barker_, Feb 21 2015: (Start)
%F A204240 a(n) = -10*a(n-1)-25*a(n-2).
%F A204240 G.f. -x*(4*x-1) / (5*x+1)^2.
%F A204240 (End)
%t A204240 f[i_, j_] := Max[3 i - 2 j, 3 j - 2 i];
%t A204240 m[n_] := Table[f[i, j], {i, 1, n}, {j, 1, n}]
%t A204240 TableForm[m[8]] (* 8x8 principal submatrix *)
%t A204240 Flatten[Table[f[i, n + 1 - i],
%t A204240   {n, 1, 12}, {i, 1, n}]]     (* A204158 *)
%t A204240 Table[Det[m[n]], {n, 1, 22}]  (* A204240 *)
%t A204240 Permanent[m_] :=
%t A204240   With[{a = Array[x, Length[m]]},
%t A204240    Coefficient[Times @@ (m.a), Times @@ a]];
%t A204240 Table[Permanent[m[n]], {n, 1, 14}]  (* A204241 *)
%o A204240 (PARI) vector(20, n, matdet(matrix(n, n, i, j, max(3*i-2*j, 3*j-2*i)))) \\ _Colin Barker_, Feb 21 2015
%Y A204240 Cf. A204158, A204241.
%K A204240 sign
%O A204240 1,2
%A A204240 _Clark Kimberling_, Jan 13 2012