A351690 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.

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

Offset

1,2

Links

Table of n, a(n) for n=1..23.

Leonard E. Dickson, Problem 142, The American Mathematical Monthly, Vol. 14, No. 5 (May, 1907), pp. 107-108.

Eric Weisstein's World of Mathematics, Perfect Difference Set

Formula

a(n) = 2*(n*(n-1)+1)*A058241(n) for n >= 3. - Pontus von Brömssen, May 09 2022

Prog

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

Crossrefs

Cf. A058241, A353077.

Sequence in context: A320826 A322199 A192882 * A056076 A117133 A238226

Adjacent sequences: A351687 A351688 A351689 * A351691 A351692 A351693

Keyword

nonn,more

Author

Michel Marcus, May 05 2022

Extensions

Name edited by Pontus von Brömssen, May 07 2022

a(1)-a(2) and a(8)-a(23) (based on data for A058241) from Pontus von Brömssen, May 09 2022

Status

approved