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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 Table of n, a(n) for n=1..96. Onno Cain, Gaussian Integers, Rings, Finite Fields, and the Magic Square of Squares, arXiv:1908.03236 [math.RA], 2019. 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 Adjacent sequences: A352617 A352618 A352619 * A352621 A352622 A352623 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.)