A382328 Maximum possible product of differences of every pair in a set of nonnegative integers with sum n.

1, 1, 2, 3, 6, 12, 20, 48, 120, 240, 540, 1440, 4320, 11520, 30240, 64512, 207360, 725760, 2419200, 7257600, 17418240, 39191040, 174182400, 696729600, 2786918400, 9405849600, 25082265600, 65840947200, 182891520000, 1003290624000, 4514807808000, 21069103104000

Offset: 0

Author

Zhao Hui Du, Mar 21 2025

Keywords

• nonn

Comments

It seems that for n>=45, if m(m+1)/2<=n<(m+1)(m+2)/2, the set to provide the maximum product has m+1 elements, such as for n=46, the maximum product is reached by set {0,1,2,3,4,5,6,7,8,10}.

Examples

			For n=7, the nonnegative integer set {0,1,2,4} has sum 7 and the product of number pairs is (1-0)*(2-0)*(4-0)*(2-1)*(4-1)*(4-2)=48 which is larger than any other sets with sum 7, so a(7)=48.
		

Links

• Chinese BBS, Find the heap array with the largest product of the differences between the two pairs in 2025

Crossrefs

Cf. A002620.