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A304680
Total number of tilings of Ferrers-Young diagrams using dominoes and at most one monomino summed over all partitions of n.
2
1, 1, 2, 6, 6, 23, 16, 76, 42, 239, 106, 688, 268, 1931, 650, 5266, 1580, 13861, 3750, 35810, 8862, 91065, 20598, 226914, 47776, 559271, 109248, 1360152, 248966, 3270429, 562630, 7785974, 1264780, 18378067, 2823958, 43007532, 6282198, 99892837, 13884820
OFFSET
0,3
MAPLE
h:= proc(l, f, t) 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), t))
else for k from nops(l) while l[k]>0 by -1 do od;
`if`(t, h(subsop(k=1, l), f, false), 0)+
`if`(nops(f)>0 and f[1]>=k, h(subsop(k=2, l), f, t), 0)+
`if`(k>1 and l[k-1]=0, h(subsop(k=1, k-1=1, l), f, t), 0)
fi
end:
g:= l-> (t-> `if`(l=[], 1, h([0$l[1]], subsop(1=[][], l),
is(t, odd))))(add(i, i=l)):
b:= (n, i, l)-> `if`(n=0 or i=1, g([l[], 1$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
Bisection (even part) gives A304662.
Cf. A304677.
Sequence in context: A119551 A100634 A242527 * A367765 A325803 A130865
KEYWORD
nonn
AUTHOR
Alois P. Heinz, May 16 2018
STATUS
approved