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%I A329871 #12 Dec 19 2019 14:20:04
%S A329871 1,2,10,55,754,18853,82931,70143802,11087020614,3243227117597,
%T A329871 1772826333285009,1806938280429412270,3430002591378184399879,
%U A329871 12137184871791092506807847,80047171080361800628780500638,983838070049011459232146327319193
%N A329871 Number of static n X n placements of water source-blocks in Minecraft.
%C A329871 In Minecraft worlds, a source block of water can be reacted with another source block, two blocks away, linearly or diagonally. This reaction creates a third "infinite" source block in the unoccupied intermediate block or blocks, so called because if the intermediate water source is destroyed or picked up by a player using a bucket, it will immediately regenerate itself.
%C A329871 A placement of water at several positions in an n X n board is said to be static if no infinite water sources are created that are not already present. In particular, the total quantity of water in the system is held constant.
%H A329871 EthosLab, <a href="https://youtu.be/9uIRD9sMBU0">Minecraft - Tutorial: Water</a>
%H A329871 Gus Wiseman, <a href="/A329871/a329871.png">The a(3) = 55 static placements of water source-blocks (black = water).</a>
%H A329871 Christopher Cormier, <a href="/A329871/a329871.cs.txt">C# Program</a>
%t A329871 vdist[v_,w_]:=Total[Abs[v-w]];
%t A329871 flowdown[prs_]:=Union[prs,With[{ovs=Select[Subsets[prs,{2}],vdist@@#==2&]},Union@@Function[{v,w},Select[Tuples[{Range[Min@@Union[First/@prs],Max@@Union[First/@prs]],Range[Min@@Union[Last/@prs],Max@@Union[Last/@prs]]}],vdist[v,#]==1&&vdist[w,#]==1&]]@@@ovs]];
%t A329871 Table[Length[Select[Subsets[Tuples[Range[n],2]],flowdown[#]==#&]],{n,0,3}]
%Y A329871 Dominates A273461.
%Y A329871 The one-dimensional case is A005251.
%Y A329871 Cf. A002416, A006498, A027624, A114901.
%K A329871 nonn
%O A329871 0,2
%A A329871 _Gus Wiseman_, Nov 26 2019
%E A329871 a(5)-a(6) from _Christopher Cormier_, Dec 10 2019
%E A329871 a(7)-a(15) from _Christopher Cormier_, Dec 19 2019

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