A246109 Number of inequivalent 8 X 8 matrices with entries from [n], where equivalence means permutations of rows or columns.

0, 1, 14685630688, 2130536585704570302966, 209493560585995285291677153144, 333504381764054807093590006199733915, 38963096281905114770318673967657388979120, 750304814691805977574386038534306614497574954, 3861175753082201291221743022346066208381644388448

Offset: 0

Author

Alois P. Heinz, Aug 13 2014

Keywords

• nonn

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

Crossrefs

Row n=8 of A246106.

Programs

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(8):
seq(a(n), n=0..10);

Formula

a(n) = 1/8!^2*(n^62 +56*n^54 +784*n^48 +644*n^46 +11760*n^42 +6272*n^40 +48020*n^38 +36064*n^36 +309680*n^34 +176400*n^32 +1060423*n^30 +423360*n^28 +4877264*n^26 +4845120*n^24 [phone]*n^22 [phone]*n^20 [phone]*n^18 [phone]*n^16 [phone]*n^14 [phone]*n^12 [phone]*n^10 [phone]*n^8 [phone]*n^6 [phone]*n^4 [phone]*n^2 [phone])*n^2.