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A323862 Table read by antidiagonals where A(n,k) is the number of n X k binary arrays in which both the sequence of rows and the sequence of columns are (independently) aperiodic.

%I A323862 #11 Jan 19 2023 22:36:03
%S A323862 2,2,2,6,10,6,12,54,54,12,30,228,498,228,30,54,990,4020,4020,990,54,
%T A323862 126,3966,32730,65040,32730,3966,126,240,16254,261522,1047540,1047540,
%U A323862 261522,16254,240,504,65040,2097018,16768860,33554370,16768860,2097018,65040,504
%N A323862 Table read by antidiagonals where A(n,k) is the number of n X k binary arrays in which both the sequence of rows and the sequence of columns are (independently) aperiodic.
%C A323862 A sequence of length n is aperiodic if all n rotations of its entries are distinct.
%H A323862 Andrew Howroyd, <a href="/A323862/b323862.txt">Table of n, a(n) for n = 1..1275</a>
%F A323862 A(n,k) = Sum_{d|n, e|k} mu(d) * mu(e) * 2^((n/d) * (k/e)).
%e A323862 Array begins:
%e A323862         2        2        6       12       30
%e A323862         2       10       54      228      990
%e A323862         6       54      498     4020    32730
%e A323862        12      228     4020    65040  1047540
%e A323862        30      990    32730  1047540 33554370
%t A323862 nn=5;
%t A323862 a[n_,k_]:=Sum[MoebiusMu[d]*MoebiusMu[e]*2^(n/d*k/e),{d,Divisors[n]},{e,Divisors[k]}];
%t A323862 Table[a[n-k,k],{n,nn},{k,n-1}]
%o A323862 (PARI) A(n,k) = {sumdiv(n, d, sumdiv(k,e, moebius(d) * moebius(e) * 2^((n/d) * (k/e))))} \\ _Andrew Howroyd_, Jan 19 2023
%Y A323862 First and last columns are A027375. Main diagonal is A265627.
%Y A323862 Cf. A000031, A000740, A001037, A179043, A323351.
%Y A323862 Cf. A323860, A323861, A323863, A323864, A323865, A323867, A323869.
%K A323862 nonn,tabl
%O A323862 1,1
%A A323862 _Gus Wiseman_, Feb 04 2019