A204238 - OEIS

%I #14 Feb 21 2015 11:47:39

%S 2,-17,104,-560,2816,-13568,63488,-290816,1310720,-5832704,25690112,

%T -112197632,486539264,-2097152000,8992587776,-38386270208,

%U 163208757248,-691489734656,2920577761280,-12300786335744,51677046505472,-216603790671872,905997581287424

%N Determinant of the n-th principal submatrix of A204237.

%H Colin Barker, <a href="/A204238/b204238.txt">Table of n, a(n) for n = 1..100</a>

%F Conjectures from _Colin Barker_, Feb 21 2015: (Start)

%F a(n) = -8*a(n-1)-16*a(n-2).

%F G.f. -x*(x-2) / (4*x+1)^2.

%F (End)

%t f[i_, j_] := Max[3 i - j, 3 j - i];

%t m[n_] := Table[f[i, j], {i, 1, n}, {j, 1, n}]

%t TableForm[m[8]] (* 8x8 principal submatrix *)

%t Flatten[Table[f[i, n + 1 - i],

%t   {n, 1, 12}, {i, 1, n}]]     (* A204237 *)

%t Table[Det[m[n]], {n, 1, 22}]  (* A204238 *)

%t Permanent[m_] :=

%t   With[{a = Array[x, Length[m]]},

%t    Coefficient[Times @@ (m.a), Times @@ a]];

%t Table[Permanent[m[n]], {n, 1, 14}] (* A204239 *)

%o (PARI) vector(20, n, matdet(matrix(n, n, i, j, max(3*i-j, 3*j-i)))) \\ _Colin Barker_, Feb 21 2015

%Y Cf. A204237, A204239.

%K sign

%O 1,1

%A _Clark Kimberling_, Jan 13 2012