

A352620


Irregular triangle read by rows which are rows of successive n X n matrices M(n) with entries M(n)[i,j] = i*j mod n+1.


3



1, 1, 2, 2, 1, 1, 2, 3, 2, 0, 2, 3, 2, 1, 1, 2, 3, 4, 2, 4, 1, 3, 3, 1, 4, 2, 4, 3, 2, 1, 1, 2, 3, 4, 5, 2, 4, 0, 2, 4, 3, 0, 3, 0, 3, 4, 2, 0, 4, 2, 5, 4, 3, 2, 1, 1, 2, 3, 4, 5, 6, 2, 4, 6, 1, 3, 5, 3, 6, 2, 5, 1, 4, 4, 1, 5, 2, 6, 3, 5, 3, 1, 6, 4, 2, 6, 5, 4, 3, 2, 1, 1, 2, 3, 4, 5
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,3


COMMENTS

Each matrix represents all possible products between the elements of Z_(n+1), where Z_k is the ring of integers mod k.
Those matrices are symmetric.
The first row is equal to the first column which is equal to 1,2,...,n.


LINKS



EXAMPLE

Matrices begin:
n=1: 1,
n=2: 1, 2,
2, 1,
n=3: 1, 2, 3,
2, 0, 2,
3, 2, 1,
n=4: 1, 2, 3, 4,
2, 4, 1, 3,
3, 1, 4, 2,
4, 3, 2, 1;
For example, the 6 X 6 matrix generated by Z_7 is the following:
1 2 3 4 5 6
2 4 6 1 3 5
3 6 2 5 1 4
4 1 5 2 6 3
5 3 1 6 4 2
6 5 4 3 2 1
The trace of this matrix is 14 = A048153(7).


MATHEMATICA

Flatten[Table[Table[Mod[k*Table[i, {i, 1, p  1}], p], {k, 1, p  1}], {p, 1, 10}]]


CROSSREFS



KEYWORD

nonn,tabf


AUTHOR



STATUS

approved



