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

0,3

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}.

Links

Table of n, a(n) for n=0..31.

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

Example

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.

Crossrefs

Cf. A002620.

Sequence in context: A079708 A096571 A227940 * A081156 A326172 A082877

Adjacent sequences: A382325 A382326 A382327 * A382329 A382330 A382331

Keyword

nonn

Author

Zhao Hui Du, Mar 21 2025

Status

approved