login
A368986
a(n) = sum of the origin-to-boundary graph-distances of all partitions of n.
2
0, 1, 2, 4, 8, 12, 21, 32, 50, 73, 107, 152, 219, 302, 419, 567, 771, 1027, 1374, 1806, 2375, 3083, 3999, 5136, 6597, 8398, 10676, 13477, 16981, 21260, 26584, 33057, 41049, 50738, 62605, 76930, 94374, 115330, 140704, 171106, 207732, 251460, 303919, 366335, 440880, 529298
OFFSET
0,3
COMMENTS
The origin-to-boundary graph-distance (see A325188) is the side length of the maximum triangular partition contained inside the Ferrer's diagram of the partition. a(n) is the sum of the side lengths over all partitions of n.
FORMULA
a(n) = Sum_{k=1..n} k*A325188(n,k).
PROG
(PARI) a(n)={my(s=0); forpart(p=n, my(w=#p); for(i=1, #p, w=min(w, #p-i+p[i])); s += w); s}
CROSSREFS
KEYWORD
nonn
AUTHOR
Andrew Howroyd, Jan 12 2024
STATUS
approved