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A089924 Number of plane partitions of n with 3 or more columns.

%I A089924 #33 Feb 03 2025 14:37:15
%S A089924 0,0,1,3,8,19,41,85,167,319,588,1066,1880,3272,5588,9431,15686,25841,
%T A089924 42070,67926,108634,172467,271643,425109,660756,1021170,1568905,
%U A089924 2398059,3646437,5519025,8314623,12473538,18634748,27731820,41113453,60735830,89411503,131193675
%N A089924 Number of plane partitions of n with 3 or more columns.
%C A089924 Because of symmetry of the 3-dimensional-Ferrers plots, this sequence also counts the plane partitions with 3 or more rows and the plane partitions with maximal element >= 3
%H A089924 Alois P. Heinz, <a href="/A089924/b089924.txt">Table of n, a(n) for n = 1..5000</a>
%H A089924 Wouter Meeussen, <a href="/A094504/a094504_1.txt">Mma functions for plane and solid partitions</a>
%e A089924 a(4)=3:
%e A089924   1111 111 211
%e A089924   .... 1.. ...
%p A089924 b:= proc(n, k) option remember; `if`(n=0, 1, add(add(min(d, k)
%p A089924       *d, d=numtheory[divisors](j))*b(n-j, k), j=1..n)/n)
%p A089924     end:
%p A089924 a:= n-> b(n, infinity)-b(n,2):
%p A089924 seq(a(n), n=1..50);  # _Alois P. Heinz_, Sep 24 2018
%t A089924 (* planepartitions[] : see link *); Table[Count[planepartitions[n], q_ /; Length[First[q]] >= 3], {n, 12}]
%Y A089924 Cf. A000219, A000991, A091357.
%K A089924 nonn
%O A089924 1,4
%A A089924 _Wouter Meeussen_, Jan 11 2004
%E A089924 a(21)-a(27) from _Vaclav Kotesovec_, May 05 2018
%E A089924 a(28)-a(38) from _Alois P. Heinz_, Sep 24 2018