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A204238 Determinant of the n-th principal submatrix of A204237.

%I A204238 #14 Feb 21 2015 11:47:39
%S A204238 2,-17,104,-560,2816,-13568,63488,-290816,1310720,-5832704,25690112,
%T A204238 -112197632,486539264,-2097152000,8992587776,-38386270208,
%U A204238 163208757248,-691489734656,2920577761280,-12300786335744,51677046505472,-216603790671872,905997581287424
%N A204238 Determinant of the n-th principal submatrix of A204237.
%H A204238 Colin Barker, <a href="/A204238/b204238.txt">Table of n, a(n) for n = 1..100</a>
%F A204238 Conjectures from _Colin Barker_, Feb 21 2015: (Start)
%F A204238 a(n) = -8*a(n-1)-16*a(n-2).
%F A204238 G.f. -x*(x-2) / (4*x+1)^2.
%F A204238 (End)
%t A204238 f[i_, j_] := Max[3 i - j, 3 j - i];
%t A204238 m[n_] := Table[f[i, j], {i, 1, n}, {j, 1, n}]
%t A204238 TableForm[m[8]] (* 8x8 principal submatrix *)
%t A204238 Flatten[Table[f[i, n + 1 - i],
%t A204238   {n, 1, 12}, {i, 1, n}]]     (* A204237 *)
%t A204238 Table[Det[m[n]], {n, 1, 22}]  (* A204238 *)
%t A204238 Permanent[m_] :=
%t A204238   With[{a = Array[x, Length[m]]},
%t A204238    Coefficient[Times @@ (m.a), Times @@ a]];
%t A204238 Table[Permanent[m[n]], {n, 1, 14}] (* A204239 *)
%o A204238 (PARI) vector(20, n, matdet(matrix(n, n, i, j, max(3*i-j, 3*j-i)))) \\ _Colin Barker_, Feb 21 2015
%Y A204238 Cf. A204237, A204239.
%K A204238 sign
%O A204238 1,1
%A A204238 _Clark Kimberling_, Jan 13 2012