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

0,3

Links

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

Formula

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

Example

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

Prog

(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(m<n, A319648(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

Crossrefs

Row sums of A092288.

Cf. A000219.

Sequence in context: A270463 A183898 A225865 * A111715 A024525 A209536

Adjacent sequences: A319645 A319646 A319647 * A319649 A319650 A319651

Keyword

nonn

Author

Alois P. Heinz, Sep 25 2018

Status

approved