A357421 a(n) is the hafnian of the 2n X 2n symmetric matrix whose generic element M[i,j] is equal to the digital root of i*j.
1, 2, 54, 1377, 55350, 4164534, 217595322, 11974135554, 999599777190, 150051627647010, 11873389098337236
Offset: 0
Examples
a(3) = 1377:
1, 2, 3, 4, 5, 6;
2, 4, 6, 8, 1, 3;
3, 6, 9, 3, 6, 9;
4, 8, 3, 7, 2, 6;
5, 1, 6, 2, 7, 3;
6, 3, 9, 6, 3, 9.
Links
- Wikipedia, Hafnian
- Wikipedia, Symmetric matrix
Crossrefs
Programs
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Mathematica
M[i_, j_, n_] := If[i*j == 0, 0, 1 + Mod[i*j - 1, 9]]; a[n_] := Sum[Product[M[Part[PermutationList[s, 2 n], 2 i - 1], Part[PermutationList[s, 2 n], 2 i], 2 n], {i, n}], {s, SymmetricGroup[2 n] // GroupElements}]/(n!*2^n); Array[a, 6, 0]
Extensions
a(6)-a(10) from Pontus von Brömssen, Oct 15 2023