This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A002974 M3304 #29 Jan 23 2019 19:59:42
%S A002974 1,1,4,7,11,20,35,59,99,165,270,443,723,1161,1861,2961,4654,7279,
%T A002974 11317,17476,26879,41132,62601,94878,143172,215115,321995,480216,
%U A002974 713655,1057192
%N A002974 Number of restricted solid partitions of n.
%C A002974 Definition, based on Math. Review MR0297583: By a solid partition of n is meant a 3-dimensional arrangement of positive integers N(x,y,z) satisfying the conditions (i) the integer N(x,y,z) is located at the point with Cartesian coordinates (x,y,z); N(x,y,z) is defined only for certain integers x,y,z >= 0, and (ii) if N(x,y,z) is defined and 0 <= x' <= x, 0 <= y' <= y, 0 <= z' <= z then N(x,y,z) is defined and N(x',y',z') <= N(x,y,z). A solid partition is said to correspond to an (ordinary) partition of n=n_1+n_2+...+n_t, n_k>0, if there is a one-to-one correspondence between the summands n_k and the points (x_k,y_k,z_k) for which N is defined so that n_k=N(x_k,y_k,z_k). Finally, a restricted solid partition is a solid partition such that x'<=x, y'<=y, z'<=z and N(x',y',z')=N(x,y,z) implies x'=x, y'=y, z'=z.
%C A002974 Alternatively, a restricted solid partition is an infinite three-dimensional array of nonnegative integers summing to n such that all one-dimensional sections are strictly decreasing until they become all zeros. - _Gus Wiseman_, Jan 22 2019
%D A002974 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A002974 H. Gupta, <a href="http://dx.doi.org/10.1016/0097-3165(72)90018-0">Restricted solid partitions</a>, J. Combin. Theory, A 13 (1972), 140-144.
%e A002974 From _Gus Wiseman_, Jan 22 2019: (Start)
%e A002974 The a(1) = 1 through a(6) = 20 restricted solid partitions, represented as chains of chains of integer partitions:
%e A002974 ((1)) ((2)) ((3)) ((4)) ((5)) ((6))
%e A002974 ((21)) ((31)) ((32)) ((42))
%e A002974 ((2)(1)) ((3)(1)) ((41)) ((51))
%e A002974 ((2))((1)) ((21)(1)) ((3)(2)) ((321))
%e A002974 ((3))((1)) ((4)(1)) ((4)(2))
%e A002974 ((21))((1)) ((31)(1)) ((5)(1))
%e A002974 ((2)(1))((1)) ((3))((2)) ((31)(2))
%e A002974 ((4))((1)) ((32)(1))
%e A002974 ((31))((1)) ((41)(1))
%e A002974 ((3)(1))((1)) ((4))((2))
%e A002974 ((21)(1))((1)) ((5))((1))
%e A002974 ((31))((2))
%e A002974 ((3)(2)(1))
%e A002974 ((32))((1))
%e A002974 ((41))((1))
%e A002974 ((3)(1))((2))
%e A002974 ((3)(2))((1))
%e A002974 ((4)(1))((1))
%e A002974 ((31)(1))((1))
%e A002974 ((3))((2))((1))
%e A002974 (End)
%t A002974 srcplptns[n_]:=Join@@Table[Select[Tuples[IntegerPartitions/@ptn],And[And@@(GreaterEqual@@@Transpose[PadRight[#]]),And@@Greater@@@#,And@@(Greater@@@DeleteCases[Transpose[PadRight[#]],0,{2}])]&],{ptn,IntegerPartitions[n]}];
%t A002974 srcsolids[n_]:=Join@@Table[Select[Tuples[srcplptns/@y],And[And@@(GreaterEqual@@@Transpose[Join@@@(PadRight[#,{n,n}]&/@#)]),And@@(Greater@@@DeleteCases[Transpose[Join@@@(PadRight[#,{n,n}]&/@#)],0,{2}])]&],{y,IntegerPartitions[n]}]
%t A002974 Table[Length[srcsolids[n]],{n,10}] (* _Gus Wiseman_, Jan 23 2019 *)
%Y A002974 Cf. A000219, A000293 (solid partitions), A000334, A001970, A114736 (restricted plane partitions), A117433 (strict plane partitions), A321662, A323657 (strict solid partitions).
%K A002974 nonn,more
%O A002974 1,3
%A A002974 _N. J. A. Sloane_
%E A002974 More terms from _Sean A. Irvine_, Dec 15 2014