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 A096577 #24 Jul 28 2025 00:01:32
%S A096577 1,0,0,0,1,0,1,0,2,0,2,0,2,0,4,1,5,0,7,1,7,0,14
%N A096577 Number of fixed points of solid partitions under 'time-lapse' operation.
%C A096577 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 planes to project into, together with the starting solid partition, that makes four 'isomers'.
%H A096577 Wouter Meeussen, <a href="/A094504/a094504_1.txt">Mma functions for plane and solid partitions</a>
%e A096577 Solid partition [{{3,1,1,1},{3}},{{2,1}},{{1}},{{1}},{{1}}] lapses (L) into
%e A096577 [{{4,1},{2},{1},{1},{1}},{{1,1},{1}},{{1,1}}], then into
%e A096577 [{{2,1,1,1,1},{2,1},{2}},{{1,1}},{{1}},{{1}}], further into
%e A096577 [{{5,2,1},{2},{1},{1}},{{1,1,1}}] and returns after L^4 to
%e A096577 [{{3,1,1,1},{3}},{{2,1}},{{1}},{{1}},{{1}}].
%t A096577 (* See link above. *)
%t A096577 Tr/@Table[Count[solidformBTK[par],arg_z/;lapse[arg]==arg],{n,20},{par,IntegerPartitions[n]}] (* _Wouter Meeussen_, Feb 05 2025 *)
%Y A096577 Cf. A000293, A094504, A094508, A096272, A096573, A096574, A096575, A096576, A096578, A096579, A096580, A096581, A119266.
%K A096577 nonn,hard,more
%O A096577 1,9
%A A096577 _Wouter Meeussen_, Jun 27 2004
%E A096577 a(16)-a(23) from _Wouter Meeussen_, Mar 19 2025