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

Terms

a(0) =0a(1) =1a(2) =2a(3) =4a(4) =8a(5) =12a(6) =21a(7) =32a(8) =50a(9) =73a(10) =107a(11) =152a(12) =219a(13) =302a(14) =419a(15) =567a(16) =771a(17) =1027a(18) =1374a(19) =1806a(20) =2375a(21) =3083a(22) =3999a(23) =5136a(24) =6597a(25) =8398a(26) =10676a(27) =13477a(28) =16981a(29) =21260