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A369396 a(n) is the maximal sum of the elements of A^3 where A is a square matrix of size n whose elements are a permutation of {1, 2, ..., n^2}. 2
1, 290, 12761, 203336, 1797702, 10816592, 49651016, 186570817, 601081822 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
a(10) >= 1714111353.
The solutions up to and including n=8 meet the same criteria (a) to (d) from para 2.2 of Fried and Mansour (2023) for the square of the matrices. See the comment in A368539. However, the trace of the optimal matrices is larger than in the case of squared matrices. When n=9, the row and column totals for the same index are no longer the same, but 4 of these totals differ by 2. See linked file.
LINKS
Sela Fried and Toufik Mansour, On the maximal sum of the entries of a matrix power, arXiv:2308.00348 [math.CO], 2023.
Hugo Pfoertner, Examples of Solutions found by Simulated Annealing, for n = 2-10, Feb 01, 2024.
EXAMPLE
a(2) = 290: A = [1, 2; A^3 = [37, 54;
3, 4] 81, 118]
.
a(3) = 12761: A = [1, 3, 4; A^3 = [ 445, 823, 1076;
2, 6, 8; 890, 1646, 2152;
5, 7, 9] 1089, 2011, 2629]
.
a(4) = 203336: A = [1, 2, 4, 7; A^3 = [2563, 5197, 6803, 7793;
3, 8, 9, 12; 5535, 11219, 14682, 16806;
5, 10, 13, 14; 7117, 14421, 18874, 21598;
6, 11, 15, 16] 8118, 16448, 21528, 24634]
CROSSREFS
Cf. A368539.
Sequence in context: A186547 A237741 A335613 * A186548 A091740 A098250
KEYWORD
nonn,hard,more
AUTHOR
Hugo Pfoertner, Jan 22 2024
STATUS
approved

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Last modified April 17 23:23 EDT 2024. Contains 371767 sequences. (Running on oeis4.)