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A304677 Total number of tilings of Ferrers-Young diagrams using dominoes and monominoes summed over all partitions of n. 2
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 (list; graph; refs; listen; history; text; internal format)



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


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)



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);


Cf. A304662, A304680.

Sequence in context: A099615 A114618 A067758 * A214418 A164342 A034527

Adjacent sequences:  A304674 A304675 A304676 * A304678 A304679 A304680




Alois P. Heinz, May 16 2018



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Last modified December 14 17:55 EST 2019. Contains 329979 sequences. (Running on oeis4.)