A319648 Total number of parts in all plane partitions of n.

0, 1, 5, 14, 38, 85, 196, 401, 830, 1615, 3119, 5802, 10718, 19246, 34276, 59889, 103656, 176801, 299025, 499732, 828638, 1360696, 2218128, 3586194, 5759839, 9184715, 14557974, 22929745, 35916469, 55942850, 86695329, 133671740, 205144324, 313380895, 476667370

Offset: 0

Author

Alois P. Heinz, Sep 25 2018

Keywords

• nonn

Examples

			The plane partitions of 2 are [2], [1 1] and [1; 1]. There is a total of a(2) = 5 parts. - _M. F. Hasler_, Sep 27 2018
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..50

Crossrefs

Row sums of A092288.

Cf. A000219.

Programs

PARI

A319648(n)={vecsum(apply(pp->vecsum(apply(p->#p,pp)),PlanePartitions(n)))} \\ See A091298 for PlanePartitions(). For illustration mainly, becomes slow for n > 15. - M. F. Hasler, Sep 27 2018

PARI

M319648=[]; A319648(n,L=0,s)={if(L, n>1||return([1,1]); #L>2||(s=setsearch(M319648,[[n,L],[]],1))>#M319648|| M319648[s][1]!=[n,L]|| return(M319648[s][2]); my(S=[1,n]); for(m=2,n, forpart(P=m, vecmin(L-Vecrev(P,#L))<0&&next; S+=if(mA319648(n-m,Vecrev(P))*[1,#P;0,1],[1,#P]),L[1],#L)); #L>2|| M319648=setunion(M319648,[[[n,L],S]]); S, my(S=n); n>1&& forpart(P=n,S+=#P); for(m=2,n-1,forpart(P=m,S+=A319648(n-m,Vecrev(P))*[#P,1]~));S)} \\ M. F. Hasler, Sep 30 2018

Formula

a(n) = Sum_{k=1..n} k*A091298(n,k). - M. F. Hasler, Sep 27 2018