A242861 Triangle T(n,k) by rows: number of ways k dominoes can be placed on an n X n chessboard, k>=0.
1, 1, 1, 4, 2, 1, 12, 44, 56, 18, 1, 24, 224, 1044, 2593, 3388, 2150, 552, 36, 1, 40, 686, 6632, 39979, 157000, 407620, 695848, 762180, 510752, 192672, 35104, 2180, 1, 60, 1622, 26172, 281514, 2135356, 11785382, 48145820, 146702793, 333518324, 562203148
Offset: 0
Examples
Triangle starts: 1 1 1 4 2 1 12 44 56 18 1 24 224 1044 2593 3388 2150 552 36 1 40 686 6632 39979 157000 407620 695848 762180 510752 192672 35104 2180 ...
Links
- Alois P. Heinz, Rows n = 0..14, flattened
- Ralf Stephan, Two dominoes on the 3x3 chessboard, illustration of T(3,2)=44.
- Eric Weisstein's World of Mathematics, Grid Graph
- Eric Weisstein's World of Mathematics, Matching-Generating Polynomial
- Wikipedia, Matching polynomial
- Index entries for sequences related to dominoes
- Index entries for sequences related to matchings
Programs
-
Maple
b:= proc(n, l) option remember; local k; if n=0 then 1 elif min(l[])>0 then b(n-1, map(h->h-1, l)) else for k while l[k]>0 do od; expand(`if`(n>1, x*b(n, subsop(k=2, l)), 0) +`if`(k -
Mathematica
b[n_, l_List] := b[n, l] = Module[{k}, Which[n == 0, 1, Min[l]>0, b[n-1, l-1], True, For[k=1, l[[k]]>0, k++]; Expand[If[n>1, x*b[n, ReplacePart[l, k -> 2]], 0] + If[k -
Sage
def T(n,k): G = Graph(graphs.Grid2dGraph(n,n)) G.relabel() mu = G.matching_polynomial() return abs(mu[n^2-2*k])
Comments