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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)
 OFFSET 0,3 LINKS 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: A099615 A114618 A067758 * A214418 A164342 A034527 Adjacent sequences:  A304674 A304675 A304676 * A304678 A304679 A304680 KEYWORD nonn AUTHOR Alois P. Heinz, May 16 2018 STATUS approved

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