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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
Matt Parker and Brady Haran, Finite Fields & Return of The Parker Square, Numberphile video (Oct 7, 2021).
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
Cf. A048153 (traces), A349099 (permanents), A160255 (sum entries), A088922 (ranks).
Cf. A074930.
Sequence in context: A370221 A098281 A207324 * A103343 A085263 A115092
KEYWORD
nonn,tabf
AUTHOR
Luca Onnis, Mar 24 2022
STATUS
approved

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Last modified June 22 10:49 EDT 2024. Contains 373570 sequences. (Running on oeis4.)