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A368985
a(n) = sum of the side lengths of the minimum containing squares of all partitions of n.
3
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
0,3
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
FORMULA
a(n) = Sum_{k>=1} k*A096771(n,k).
PROG
(PARI) a(n)={my(s=0); if(n, forpart(p=n, s += max(#p, p[#p]))); s}
CROSSREFS
KEYWORD
nonn
AUTHOR
Andrew Howroyd, Jan 12 2024
STATUS
approved