A304677 Total number of tilings of Ferrers-Young diagrams using dominoes and monominoes summed over all partitions of n.

1, 1, 4, 9, 27, 60, 170, 377, 996, 2288, 5715, 13002, 32321, 72864, 175137, 400039, 943454, 2133159, 4993737, 11236889, 25995341, 58480330, 133650880, 299347432, 681346296, 1519116099, 3427954877, 7631479391, 17122129103, 37958987956, 84819325972, 187405201004

Offset

0,3

Links

Table of n, a(n) for n=0..31.

Eric Weisstein's World of Mathematics, Ferrers Diagram

Wikipedia, Domino

Wikipedia, Domino tiling

Wikipedia, Ferrers diagram

Wikipedia, Partition (number theory)

Wikipedia, Polyomino

Wikipedia, Young tableau, Diagrams

Maple

h:= proc(l, f) option remember; local k; if min(l[])>0 then
     `if`(nops(f)=0, 1, h(map(x-> x-1, l[1..f[1]]), subsop(1=[][], f)))
    else for k from nops(l) while l[k]>0 by -1 do od; h(subsop(k=1, l), f)+
        `if`(nops(f)>0 and f[1]>=k, h(subsop(k=2, l), f), 0)+
        `if`(k>1 and l[k-1]=0, h(subsop(k=1, k-1=1, l), f), 0)
      fi
    end:
g:= l-> `if`(l=[], 1, h([0$l[1]], subsop(1=[][], l))):
b:= (n, i, l)-> `if`(n=0 or i=1, g([l[], 1$n]), b(n, i-1, l)
                  +b(n-i, min(n-i, i), [l[], i])):
a:= n-> b(n$2, []):
seq(a(n), n=0..23);

Crossrefs

Cf. A304662, A304680.

Sequence in context: A114618 A067758 A357752 * A214418 A164342 A034527

Adjacent sequences: A304674 A304675 A304676 * A304678 A304679 A304680

Keyword

nonn

Author

Alois P. Heinz, May 16 2018

Status

approved