A368986 a(n) = sum of the origin-to-boundary graph-distances of all partitions of n.

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

Author

Andrew Howroyd, Jan 12 2024

Keywords

• nonn

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.

Crossrefs

Cf. A325188, A325189, A325200.

Programs

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}

Formula

a(n) = Sum_{k=1..n} k*A325188(n,k).