A204235 Permanent of the n-th principal submatrix of A143182.

1, 5, 42, 632, 14124, 449652, 19200336, 1063272704, 74068997888, 6344884818304, 655635015988864, 80447681129070080, 11565193558509497088, 1925787312858332101888, 367762470538537620457472, 79847718328265949957881856, 19560087897336150724249288704

Offset: 1

Author

Clark Kimberling, Jan 13 2012

Keywords

• nonn

Comments

The n-th principal submatrix of A143182 is an n X n symmetric Toeplitz matrix whose first row consists of successive natural numbers 1, ..., n. - Stefano Spezia, Sep 23 2018

Conjecture: a(1) and a(2) are the only terms that are odd numbers. - Stefano Spezia, Oct 28 2018

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 1..35 (terms 1..14 from Clark Kimberling, terms 15..22 from Stefano Spezia)

Crossrefs

Cf. A143182.

Programs

Maple

f:= proc(n) uses LinearAlgebra;
Permanent(ToeplitzMatrix([seq(i, i=1 ..n)], n, symmetric))
end proc:
map(f, [$1..20]); # Stefano Spezia, Oct 28 2018

Mathematica

f[i_, j_] := Max[i - j + 1, j - i + 1];  (* A143182 *)
m[n_] := Table[f[i, j], {i, 1, n}, {j, 1, n}]
TableForm[m[4]] (* 4 X 4 principal submatrix *)
Table[Det[m[n]], {n, 1, 22}]  (* A001792 - signed *)
Permanent[m_] :=
  With[{a = Array[x, Length[m]]},
   Coefficient[Times @@ (m.a), Times @@ a]];
Table[Permanent[m[n]], {n, 1, 14}]  (* A204235 *)
b[i_]:=i; a[n_]:=Permanent[ToeplitzMatrix[Array[b, n], Array[b, n]]]; Array[a, 22] (* Stefano Spezia, Sep 23 2018 *)

PARI

{a(n) = matpermanent(matrix(n, n, i, j, max(i - j + 1, j - i + 1)))}
for(n=1, 20, print1(a(n), ", ")) \\ Vaclav Kotesovec, Apr 29 2019

Extensions

Extended by Stefano Spezia, Oct 28 2018