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

2, -17, 104, -560, 2816, -13568, 63488, -290816, 1310720, -5832704, 25690112, -112197632, 486539264, -2097152000, 8992587776, -38386270208, 163208757248, -691489734656, 2920577761280, -12300786335744, 51677046505472, -216603790671872, 905997581287424

Offset: 1

Author

Clark Kimberling, Jan 13 2012

Keywords

• sign

Links

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

Crossrefs

Cf. A204237, A204239.

Programs

Mathematica

f[i_, j_] := Max[3 i - j, 3 j - 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}]]     (* A204237 *)
Table[Det[m[n]], {n, 1, 22}]  (* A204238 *)
Permanent[m_] :=
  With[{a = Array[x, Length[m]]},
   Coefficient[Times @@ (m.a), Times @@ a]];
Table[Permanent[m[n]], {n, 1, 14}] (* A204239 *)

PARI

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

Formula

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

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

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

(End)