A351690 - OEIS

%I #19 May 09 2022 08:34:50

%S 1,3,14,52,42,310,0,684,584,1092,0,4788,0,7320,0,0,3276,31314,0,32004,

%T 0,0,0

%N a(n) is the number of n-subsets of [0..p-1] whose n*(n-1) differences are congruent to 1..p-1 (mod p), where p=n*(n-1)+1.

%H Leonard E. Dickson, <a href="https://doi.org/10.2307/2968498">Problem 142</a>, The American Mathematical Monthly, Vol. 14, No. 5 (May, 1907), pp. 107-108.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PerfectDifferenceSet.html">Perfect Difference Set</a>

%F a(n) = 2*(n*(n-1)+1)*A058241(n) for n >= 3. - _Pontus von Brömssen_, May 09 2022

%o (PARI) isok(n, v) = my(p=n*(n-1)+1); setbinop((x, y)->lift(Mod(x-y, p)), v, v) == [0..p-1];

%o a(n) = my(nb=0); forsubset([n^2-n+1, n], s, my(ds = apply(x->x-1, Vec(s))); if (isok(n, ds), nb++)); nb;

%Y Cf. A058241, A353077.

%K nonn,more

%O 1,2

%A _Michel Marcus_, May 05 2022

%E Name edited by _Pontus von Brömssen_, May 07 2022

%E a(1)-a(2) and a(8)-a(23) (based on data for A058241) from _Pontus von Brömssen_, May 09 2022