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 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 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS For large n the rows end in A091360 = partial sums of A000219 (count of plane partitions). 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

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Last modified June 19 17:16 EDT 2019. Contains 324222 sequences. (Running on oeis4.)