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A231642
Triangle read by rows, t(n,k) = binomial(n,k) mod n, k <= n.
1
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, 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, 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
OFFSET
1,8
COMMENTS
Rows of the form 0,0,0,...,0,1 fit prime n.
LINKS
Frank Ruskey, Carla D. Savage, and Stan Wagon, The Search for Simple Symmetric Venn Diagrams, Notices Amer. Math. Soc. 53 (2006), no. 11, 1304-1311., page 1.
EXAMPLE
Triangle begins:
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;
...
MATHEMATICA
t[n_, k_] := Mod[Binomial[n, k], n]; Table[t[n, k], {n, 14}, {k, n}] // Flatten
PROG
(PARI) t(n, k)=binomial(n, k)%n \\ Charles R Greathouse IV, Nov 12 2013
CROSSREFS
Sequence in context: A331671 A373925 A123758 * A288318 A354099 A219483
KEYWORD
nonn,tabl
AUTHOR
STATUS
approved