OFFSET
1,2
LINKS
Alois P. Heinz, Rows n = 1..50, flattened
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
KEYWORD
nonn,tabl
AUTHOR
Wouter Meeussen, Feb 01 2004
STATUS
approved