A383212 a(n) = permanent of the n-th principal submatrix of the rectangular array whose odd-numbered rows are (2,1,2,1,2,1,2,1,...) and even-numbered rows are (1,2,1,2,1,2,1,2,...).
1, 2, 5, 24, 132, 1032, 8820, 95616, 1106496, 15327360, 223560000, 3768768000, 66305952000, 1316927808000, 27127003680000, 620221722624000, 14638710417408000, 378633583448064000, 10073602372700160000, 290788929384726528000, 8609476463579013120000, 274361332654900592640000, 8946658680536444313600000
Offset: 0
Keywords
Crossrefs
Cf. A204252.
Programs
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Maple
1, seq(LinearAlgebra:-Permanent(Matrix(n,n,(i,j) -> 1 + (i+j+1 mod 2))), n=1..22); # Robert Israel, Apr 23 2025
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Mathematica
a[i_, j_] := If[EvenQ[i + j], 2, 1]; m[n_] := Table[a[i, j], {i, 1, n}, {j, 1, n}]; Join[{1}, Table[Permanent[m[n]], {n, 1, 19}]] -
PARI
a(n) = {matpermanent(matrix(n, n, i, j, 2 - (i+j)%2))}; for(n=0, 25, print1(a(n), ", ")) \\ Vaclav Kotesovec, Apr 21 2025
Extensions
a(20)-a(22) from Vaclav Kotesovec, Apr 21 2025