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

1, -14, 115, -800, 5125, -31250, 184375, -1062500, 6015625, -33593750, 185546875, -1015625000, 5517578125, -29785156250, 159912109375, -854492187500, 4547119140625, -24108886718750, 127410888671875, -671386718750000

Offset: 1

Author

Clark Kimberling, Jan 13 2012

Keywords

• sign

Links

• Colin Barker, Table of n, a(n) for n = 1..100

Crossrefs

Cf. A204158, A204241.

Programs

Mathematica

f[i_, j_] := Max[3 i - 2 j, 3 j - 2 i];
m[n_] := Table[f[i, j], {i, 1, n}, {j, 1, n}]
TableForm[m[8]] (* 8x8 principal submatrix *)
Flatten[Table[f[i, n + 1 - i],
  {n, 1, 12}, {i, 1, n}]]     (* A204158 *)
Table[Det[m[n]], {n, 1, 22}]  (* A204240 *)
Permanent[m_] :=
  With[{a = Array[x, Length[m]]},
   Coefficient[Times @@ (m.a), Times @@ a]];
Table[Permanent[m[n]], {n, 1, 14}]  (* A204241 *)

PARI

vector(20, n, matdet(matrix(n, n, i, j, max(3*i-2*j, 3*j-2*i)))) \\ Colin Barker, Feb 21 2015

Formula

Conjectures from Colin Barker, Feb 21 2015: (Start)

a(n) = -10*a(n-1)-25*a(n-2).

G.f. -x*(4*x-1) / (5*x+1)^2.

(End)