A196275 Number of column-convex permutominoes of size n.

1, 4, 22, 152, 1262, 12232, 135544, 1690080, 23417928, 356958816, 5936071344, 106944112320, 2074955738160, 43135041684288, 956498746867584, 22535656688150016, 562187777547687552, 14803856501210021376, 410341578632728752384, 11942796083017877185536, 364141566064571517418752, 11607532093950790287928320

Offset

1,2

Links

Vaclav Kotesovec, Table of n, a(n) for n = 1..200 (computed by Anthony J. Guttmann)

Nicholas R. Beaton, Filippo Disanto, Anthony J. Guttmann and Simone Rinaldi, On the enumeration of column-convex permutominoes, in FPSAC 2011, Reykjavik, Iceland DMTCS proc. AO, 2011, 111-122.

Mathematica

cecka = {}; Do[fxyz = Sum[If[h + d + w <= n, Subscript[c, h, d, w]*x^h*y^d*z^w, 0], {h, 0, n}, {d, 0, n}, {w, 0, n}]; fxyz = Simplify[fxyz /. cecka]; feq = Expand[Together[(x - y)*(z - y)*(y + y*z/(z - y)*(fxyz /. y -> z) - y^2/(z - y)*(fxyz /. z -> y) + x*y/(x - y)*(fxyz /. y -> x) - y^2/(x - y)*(fxyz /. x -> y))]]; fxyz1 = Expand[Simplify[(x - y)*(z - y)*fxyz]]; fxyz2 = 0; Do[p = fxyz1[[j]]; If[Total[Exponent[p, {x, y, z}]] <= n + 2, fxyz2 += p], {j, 1, Length[fxyz1]}]; poly2 = 0; Do[p = feq[[j]]; If[Total[Exponent[p, {x, y, z}]] <= n + 2, poly2 += p], {j, 1, Length[feq]}]; ceckanew = SolveAlways[fxyz2 == poly2, {x, y, z}][[1]]; cecka = Join[cecka, ceckanew]; gfxyz = fxyz /. cecka; , {n, 1, 15}]; Rest[CoefficientList[gfxyz /. {x -> y, z -> y}, y]] (* Vaclav Kotesovec, Jun 07 2021 *)

Crossrefs

Sequence in context: A267219 A152404 A062817 * A000307 A294346 A049376

Adjacent sequences: A196272 A196273 A196274 * A196276 A196277 A196278

Keyword

nonn

Author

N. J. A. Sloane, Sep 30 2011

Extensions

More terms from Vaclav Kotesovec, Jun 07 2021

Status

approved