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A319648 Total number of parts in all plane partitions of n. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified April 24 16:26 EDT 2019. Contains 322430 sequences. (Running on oeis4.)