A204265 Permanent of n X n matrix M with M(i,j) = (i+j) (mod 3).

2, 2, 9, 40, 144, 1032, 7824, 48816, 530712, 5619456, 50015232, 707802624, 9591229440, 112586112000, 1938416832000, 32061464064000, 469224244224000, 9509523337728000, 185772505605120000, 3261008730405888000

Offset: 1

Author

Clark Kimberling, Jan 15 2012

Keywords

• nonn

Comments

Permanent of the n-th principal submatrix of A204263.

Crossrefs

Cf. A204263.

Programs

Mathematica

f[i_, j_] := Mod[i + j, 3];
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, 14}, {i, 1, n}]]    (* A204263 *)
Permanent[m_] :=
  With[{a = Array[x, Length[m]]},
   Coefficient[Times @@ (m.a), Times @@ a]];
Table[Permanent[m[n]], {n, 1, 22}]    (* A204265 *)

PARI

matperm(M)=my(n=#M,t);sum(i=1,n!,t=numtoperm(n,i);prod(j=1,n,M[j,t[j]]));a(n)=matperm(matrix(n,n,i,j,(i+j)%3)) \\ Ralf Stephan, Oct 19 2013