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 A096578 #12 Aug 08 2025 03:26:26
%S A096578 0,0,1,1,1,2,3,6,7,11,15,25,33,48,65
%N A096578 Number of solid partitions with period (cycle length) two under 'time-lapse' operation.
%C A096578 Operation 'time lapse', or 'lapse', L, operates on a solid partition by creating a new one, layer by layer. Layer k is defined by its 3-dimensional-Ferrers plot, equal to the (existence of) elements of the solid partition with value >= k. As if taking a time-lapse picture of the solid partition, filtering out elements less than k and projecting the resulting structure (filled with ones) to the base plane. Given there are three plane to project into, together with the starting solid partition, that makezs four 'isomers'.
%H A096578 Wouter Meeussen, <a href="/A094504/a094504_1.txt">Mma functions for plane and solid partitions</a>
%e A096578 Solid partition [{{3,1,1,1},{3}},{{2,1}},{{1}},{{1}},{{1}}] lapses (L) into
%e A096578 [{{4,1},{2},{1},{1},{1}},{{1,1},{1}},{{1,1}}], then into
%e A096578 [{{2,1,1,1,1},{2,1},{2}},{{1,1}},{{1}},{{1}}], further into
%e A096578 [{{5,2,1},{2},{1},{1}},{{1,1,1}}] and returns after L^4 to
%e A096578 [{{3,1,1,1},{3}},{{2,1}},{{1}},{{1}},{{1}}]
%t A096578 (* See link above. *)
%Y A096578 Cf. A000293, A094504, A094508, A096272, A096573, A096574, A096575, A096576, A096577, A096579, A096580, A096581.
%K A096578 nonn,more
%O A096578 1,6
%A A096578 _Wouter Meeussen_, Jun 27 2004