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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 (list; graph; refs; listen; history; text; internal format)
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

Rainer Rosenthal, Table of n, a(n) for n = 1..191

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: A337527 A140840 A175158 * A233219 A288685 A068235

Adjacent sequences:  A180084 A180085 A180086 * A180088 A180089 A180090

KEYWORD

nonn

AUTHOR

Hugo Pfoertner, Aug 09 2010

STATUS

approved

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Last modified September 26 01:25 EDT 2020. Contains 337346 sequences. (Running on oeis4.)