A246111 Number of inequivalent 10 X 10 matrices with entries from [n], where equivalence means permutations of rows or columns.

0, 1, 105735224248507784, 39197947672609240635681299333726499, 122042291850117110186411151373496788803833567344, 599071101908675118606355537962231556550216893297767505350, 49613471837781303435661841941440050234912472934180371572880191904

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Index to number of inequivalent matrices modulo permutation of rows and columns

Formula

a(n) = 1/10!^2*(n^98 +90*n^88 +2025*n^80 +1740*n^78 +56700*n^72 +21600*n^70 +18900*n^68 +396900*n^66 +341100*n^64 +869400*n^62 +3969000*n^60 +126546*n^58 +20704950*n^56 +12039300*n^54 +31067820*n^52 +148602825*n^50 +42387975*n^48 +317648520*n^46 +565828200*n^44 +1281483000*n^42 +2237949000*n^40 +2984535664*n^38 +7012483800*n^36 +13249603200*n^34 +22883250880*n^32 +27251386200*n^30 +67958469720*n^28 +101700222480*n^26 +171243702000*n^24 +256351060800*n^22 +344831018400*n^20 +534080757024*n^18 +779152348800*n^16 +1222054473600*n^14 +1199867616000*n^12 +1352864851200*n^10 +2244578999040*n^8 +1451810304000*n^6 +1656953625600*n^4 +1288659456000*n^2 +418037760000)*n^2.

Maple

b:= proc(n, i) option remember; `if`(n=0, [[]],
      `if`(i<1, [], [b(n, i-1)[], seq(map(p->[p[], [i, j]],
       b(n-i*j, i-1))[], j=1..n/i)]))
    end:
a:= proc(n) unapply(add(add(x^add(add(i[2]*j[2]*
      igcd(i[1], j[1]), j=t), i=s) /mul(i[1]^i[2]*i[2]!, i=s)
      /mul(i[1]^i[2]*i[2]!, i=t), t=b(n$2)), s=b(n$2)), x)
    end(10):
seq(a(n), n=0..10);

Crossrefs

Row n=10 of A246106.

Sequence in context: A097717 A128857 A357515 * A067818 A262560 A095433

Adjacent sequences: A246108 A246109 A246110 * A246112 A246113 A246114

Keyword

nonn

Author

Alois P. Heinz, Aug 13 2014

Status

approved