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A204238
Determinant of the n-th principal submatrix of A204237.
4
2, -17, 104, -560, 2816, -13568, 63488, -290816, 1310720, -5832704, 25690112, -112197632, 486539264, -2097152000, 8992587776, -38386270208, 163208757248, -691489734656, 2920577761280, -12300786335744, 51677046505472, -216603790671872, 905997581287424
OFFSET
1,1
LINKS
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)
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 *)
PROG
(PARI) vector(20, n, matdet(matrix(n, n, i, j, max(3*i-j, 3*j-i)))) \\ Colin Barker, Feb 21 2015
CROSSREFS
Sequence in context: A129977 A213787 A105652 * A198796 A186104 A155845
KEYWORD
sign
AUTHOR
Clark Kimberling, Jan 13 2012
STATUS
approved