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A180087
Upper bound for the determinant of a matrix whose entries are a permutation of 1, ..., n^2.
3
1, 11, 450, 41021, 6865625, 1867994210, 762539814814, 441077015225642, 346335386150480625, 357017114947987625629, 470379650542113331346272, 774869480550211708169959725, 1566955892015559322525350178004
OFFSET
1,2
REFERENCES
Ortwin Gasper, Hugo Pfoertner and Markus Sigg, An Upper Bound for the Determinant of a Matrix with given Entry Sum and Square Sum, JIPAM, Journal of Inequalities in Pure and Applied Mathematics, Volume 10, Issue 3, Article 63, 2008.
LINKS
O. Gasper, H. Pfoertner and M. Sigg, An Upper Bound for the Determinant of a Matrix with given Entry Sum and Square Sum JIPAM, vol. 10, Iss. 3, art. 63, 2008.
Markus Sigg, Gasper's determinant theorem, revisited, arXiv:1804.02897 [math.CO], 2018.
FORMULA
a(n) = floor(sqrt(3*((n^5+n^4+n^3+n^2)/12)^n*(n^2+1)/(n+1))).
CROSSREFS
a(n) is an upper bound for A085000(n).
Sequence in context: A175158 A360066 A354439 * A233219 A288685 A068235
KEYWORD
nonn
AUTHOR
Hugo Pfoertner, Aug 09 2010
STATUS
approved