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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<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.

Cf. A000219, A066633.

Sequence in context: A230534 A177822 A091156 * A111964 A242351 A124324

Adjacent sequences:  A092285 A092286 A092287 * A092289 A092290 A092291

KEYWORD

nonn,tabl

AUTHOR

Wouter Meeussen, Feb 01 2004

STATUS

approved

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