A231642 - OEIS

%I #14 Jan 05 2023 11:05:09

%S 0,0,1,0,0,1,0,2,0,1,0,0,0,0,1,0,3,2,3,0,1,0,0,0,0,0,0,1,0,4,0,6,0,4,

%T 0,1,0,0,3,0,0,3,0,0,1,0,5,0,0,2,0,0,5,0,1,0,0,0,0,0,0,0,0,0,0,1,0,6,

%U 4,3,0,0,0,3,4,6,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,7,0,7,0,7,2,7,0,7,0,7,0,1

%N Triangle read by rows, t(n,k) = binomial(n,k) mod n, k <= n.

%C Rows of the form 0,0,0,...,0,1 fit prime n.

%H T. D. Noe, <a href="/A231642/b231642.txt">Rows n = 1..100 of triangle, flattened</a>

%H Frank Ruskey, Carla D. Savage, and Stan Wagon, <a href="http://www.ams.org/notices/200611/ea-wagon.pdf">The Search for Simple Symmetric Venn Diagrams</a>, Notices Amer. Math. Soc. 53 (2006), no. 11, 1304-1311., page 1.

%e Triangle begins:

%e   0;

%e   0, 1;

%e   0, 0, 1;

%e   0, 2, 0, 1;

%e   0, 0, 0, 0, 1;

%e   0, 3, 2, 3, 0, 1;

%e   0, 0, 0, 0, 0, 0, 1;

%e   ...

%t t[n_, k_] := Mod[Binomial[n,k], n]; Table[t[n, k], {n, 14}, {k, n}] // Flatten

%o (PARI) t(n,k)=binomial(n,k)%n \\ _Charles R Greathouse IV_, Nov 12 2013

%K nonn,tabl

%O 1,8

%A _Jean-François Alcover_, Nov 12 2013