A368985 a(n) = sum of the side lengths of the minimum containing squares of all partitions of n.

0, 1, 4, 8, 16, 27, 47, 72, 115, 170, 255, 364, 527, 732, 1026, 1401, 1916, 2568, 3451, 4556, 6023, 7859, 10245, 13217, 17041, 21766, 27770, 35173, 44471, 55874, 70092, 87432, 108881, 134951, 166948, 205678, 252951, 309908, 379032, 462046, 562246, 682130

Offset: 0

Author

Andrew Howroyd, Jan 12 2024

Keywords

• nonn

Comments

The minimum containing square of a partition has its side length equal to the number of parts or the size of the largest part whichever is greater. a(n) is the sum of the side lengths over all partitions of n.

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..750

Crossrefs

Cf. A096771, A115995, A182094.

Programs

PARI

a(n)={my(s=0); if(n, forpart(p=n, s += max(#p, p[#p]))); s}

Formula

a(n) = Sum_{k>=1} k*A096771(n,k).