%I A098529
%S A098529 1,3,3,3,6,6,1,3,18,3,9,24,15,3,42,38,3,10,60,69,21,6,72,153,45,6,9,114,
%T A098529 220,141,15,1,3,120,399,274,60,3,18,159,558,570,162,12,3,174,834,1029,
%U A098529 399,46,9,267,1080,1749,921,138,3
%N A098529 Triangle read by rows: T(n,k) counts plane partitions of n+1 that can 
               be 'shrunk' in k ways to a plane partition of n by removing 1 element 
               from it. Equivalently, it counts how many partitions of n+1 have 
               k different partitions of n it just covers.
%C A098529 Sequence starts 1; 3; 3,3; 6,6,1; 3,18,3; 9,24,15; 3,42,38,3; Row sums 
               are A000219= the plane partitions of n+1 apart from offset. Sum(all 
               k, k * T(n,k) ) = A090984(n) by definition. First column is A007425. 
               Row lengths are A120565. - Frank Adams-Watters (FrankTAW(AT)Netscape.net), 
               Jun 14 2006
%e A098529 T(4,1)=2 because the only plane partitions of 4+1=5 that can be shrunk 
               in only 1 way to plane partitions of 4 are {{5}} and {{1},{1},{1},
               {1},{1}}, producing {{4}} and {{1},{1},{1},{1}} respectively.
%e A098529 T(4,1)=3 because the only plane partitions of 4+1=5 that can be shrunk 
               in only 1 way to plane partitions of 4 are {{5}},{{1,1,1,1,1}} and 
               {{1},{1},{1},{1},{1}}, producing {{4}},{{1,1,1,1}} and {{1},{1},{1},
               {1}} respectively.
%t A098529 (* functions 'planepartitions' and 'coversplaneQ', see A096574 *) Table[Frequencies[Count[planepartitions[n],\
                q_/; coversplaneQ[ #, q]]&/@ planepartitions[n+1]], {n, 1, 12}]
%Y A098529 Cf. A000219, A090984, A007425, A120565.
%Y A098529 Sequence in context: A158315 A134059 A112669 this_sequence A133774 A108581 
               A073080
%Y A098529 Adjacent sequences: A098526 A098527 A098528 this_sequence A098530 A098531 
               A098532
%K A098529 more,nonn,tabf
%O A098529 0,2
%A A098529 Wouter Meeussen (wouter.meeussen(AT)pandora.be), Sep 12 2004
%E A098529 Corrected and extended by Frank Adams-Watters (FrankTAW(AT)Netscape.net), 
               Jun 14 2006
%E A098529 More terms from Wouter Meeussen (wouter.meeussen(AT)pandora.be), May 
               05 2007