A329871 Number of static n X n placements of water source-blocks in Minecraft.

1, 2, 10, 55, 754, 18853, 82931, 70143802, 11087020614, 3243227117597, 1772826333285009, 1806938280429412270, 3430002591378184399879, 12137184871791092506807847, 80047171080361800628780500638, 983838070049011459232146327319193

Offset: 0

Author

Gus Wiseman, Nov 26 2019

Keywords

• nonn

Comments

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.

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.

Links

• EthosLab, Minecraft - Tutorial: Water
• Gus Wiseman, The a(3) = 55 static placements of water source-blocks (black = water).
• Christopher Cormier, C# Program

Crossrefs

Dominates A273461.

The one-dimensional case is A005251.

Cf. A002416, A006498, A027624, A114901.

Programs

Mathematica

vdist[v_,w_]:=Total[Abs[v-w]];
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]];
Table[Length[Select[Subsets[Tuples[Range[n],2]],flowdown[#]==#&]],{n,0,3}]

Extensions

a(5)-a(6) from Christopher Cormier, Dec 10 2019

a(7)-a(15) from Christopher Cormier, Dec 19 2019