A246109 - OEIS

%I #9 May 02 2022 10:24:42

%S 0,1,14685630688,2130536585704570302966,

%T 209493560585995285291677153144,333504381764054807093590006199733915,

%U 38963096281905114770318673967657388979120,750304814691805977574386038534306614497574954,3861175753082201291221743022346066208381644388448

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

%H Alois P. Heinz, <a href="/A246109/b246109.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Mat#inequiv">Index to number of inequivalent matrices modulo permutation of rows and columns</a>

%F 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 +14721560*n^22 +17144512*n^20 +41692336*n^18 +41106688*n^16 +123789552*n^14 +139448064*n^12 +197401344*n^10 +190027776*n^8 +288610560*n^6 +239339520*n^4 +235468800*n^2 +85155840)*n^2.

%p b:= proc(n, i) option remember; `if`(n=0, [[]],

%p       `if`(i<1, [], [b(n, i-1)[], seq(map(p->[p[], [i, j]],

%p        b(n-i*j, i-1))[], j=1..n/i)]))

%p     end:

%p a:= proc(n) unapply(add(add(x^add(add(i[2]*j[2]*

%p       igcd(i[1], j[1]), j=t), i=s) /mul(i[1]^i[2]*i[2]!, i=s)

%p       /mul(i[1]^i[2]*i[2]!, i=t), t=b(n$2)), s=b(n$2)), x)

%p     end(8):

%p seq(a(n), n=0..10);

%Y Row n=8 of A246106.

%K nonn

%O 0,3

%A _Alois P. Heinz_, Aug 13 2014