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 A373457 #21 Sep 03 2024 01:16:08
%S A373457 0,0,1,3,3,4,7,11,12,17,24,34,40,54,73,100,125,164,208,270,337,428,
%T A373457 534,673,828,1033,1276,1584,1938,2385,2909,3559,4318,5252,6346,7678,
%U A373457 9230,11108,13309,15953,19034,22719,27019,32132,38084,45129,53326,62988,74200,87371
%N A373457 Number of losing integer partitions of n in the impartial combinatorial game LCTR (left column, top row).
%H A373457 Eric Gottlieb, Matjaž Krnc, and Peter Muršič, <a href="https://doi.org/10.1016/j.dam.2023.11.036">Sprague-Grundy values and complexity for LCTR, Discrete Applied Mathematics</a>, Discrete Applied Mathematics, Volume 346, 2024, Pages 154-169.
%H A373457 Eric Gottlieb, Jelena Ilić, and Matjaž Krnc, <a href="https://doi.org/10.2140/involve.2023.16.529">Some results on LCTR, an impartial game on partitions</a>, Involve, Vol. 16 2023, No. 3, pages 529-546.
%e A373457 For n = 8, the a(8) = 11 losing partitions are the six nondegenerate hooks (7,1), (6, 1, 1), (5, 1, 1, 1), (4, 1, 1, 1, 1), (3, 1, 1, 1, 1, 1), (2, 1, 1, 1, 1, 1, 1) and (5, 3), (4, 4), (3, 3, 2), (2, 2, 2, 2), (2, 2, 2, 1, 1).
%t A373457 << "Combinatorica`"
%t A373457 Mex[Ls_] :=
%t A373457 If[Ls == {}, 0, Min[Complement[Table[n, {n, 0, Length[Ls]}], Ls]]]
%t A373457 LCTRMoves[Pttn_] :=
%t A373457 Union[{Rest[Pttn],
%t A373457 TransposePartition[Rest[TransposePartition[Pttn]]]}]
%t A373457 LCTRSG[Pttn_] :=
%t A373457 If[Pttn == {}, 0, LCTRSG[Pttn] = Mex[LCTRSG /@ LCTRMoves[Pttn]]]
%t A373457 NumLosingPttns[n_] :=
%t A373457 Table[{k,
%t A373457 Length[Select[IntegerPartitions[k], LCTRSG[#] == 0 &]]}, {k, 1,
%t A373457 n}] // TableForm
%Y A373457 Cf. A000041.
%K A373457 nonn
%O A373457 1,4
%A A373457 _Eric Gottlieb_, Jun 06 2024