[go: up one dir, main page]

login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A092288
Triangle read by rows: T(n,k) = count of parts k in all plane partitions of n.
5
1, 4, 1, 11, 2, 1, 28, 7, 2, 1, 62, 15, 5, 2, 1, 137, 38, 13, 5, 2, 1, 278, 76, 28, 11, 5, 2, 1, 561, 164, 60, 26, 11, 5, 2, 1, 1080, 316, 124, 52, 24, 11, 5, 2, 1, 2051, 623, 244, 108, 50, 24, 11, 5, 2, 1, 3778, 1156, 469, 208, 100, 48, 24, 11, 5, 2, 1, 6885, 2160, 886, 404, 194, 98, 48, 24, 11, 5, 2, 1
OFFSET
1,2
COMMENTS
For large n the rows end in A091360 = partial sums of A000219 (count of plane partitions).
LINKS
M. F. Hasler, A092288, rows 1 - 18.
EXAMPLE
Triangle begins:
1;
4, 1;
11, 2, 1;
28, 7, 2, 1;
62, 15, 5, 2, 1;
137, 38, 13, 5, 2, 1;
...
MATHEMATICA
Table[Length /@ Split[Sort[Flatten[planepartitions[k]]]], {k, 12}]
PROG
(PARI) A092288_row(n, c=vector(n), m, k)={for(i=1, #n=PlanePartitions(n), for(j=1, #m=n[i], for(i=1, #k=m[j], c[k[i]]++))); c} \\ See A091298 for PlanePartitions(). See below for more efficient code.
M92288=[]; A092288(n, k, L=0)={n>1||return(if(L, [n, n==k], n==k)); if(#L&& #L<3, my(j=setsearch(M92288, [[n, k, L], []], 1)); j<=#M92288&& M92288[j][1]==[n, k, L]&& return(M92288[j][2])); my(c(p)=sum(i=1, #p, p[i]==k), S=[0, 0], t); for(m=1, n, my(P=if(L, select(p->vecmin(L-Vecrev(p, #L))>=0, partitions(m, L[1], #L)), partitions(m))); if(m<n, for(i=1, #P, t=A092288(n-m, k, Vecrev(P[i])); S+=[t[1], t[1]*c(P[i])+t[2]], S+=[#P, vecsum(apply(c, P))])); if(L, #L<3&& M92288= setunion(M92288, [[[n, k, L], S]]); S, S[2])} \\ M. F. Hasler, Sep 26 2018
CROSSREFS
Column k=1 gives A090539.
Row sums give A319648.
T(2n+1,n+1) gives A091360.
Sequence in context: A230534 A177822 A091156 * A111964 A242351 A124324
KEYWORD
nonn,tabl
AUTHOR
Wouter Meeussen, Feb 01 2004
STATUS
approved