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A210249
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Number of partitions of n in which all parts are less than n/2.
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5
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1, 0, 0, 1, 1, 3, 4, 8, 10, 18, 23, 37, 47, 71, 90, 131, 164, 230, 288, 393, 488, 653, 807, 1060, 1303, 1686, 2063, 2637, 3210, 4057, 4920, 6158, 7434, 9228, 11098, 13671, 16380, 20040, 23928, 29098, 34624, 41869, 49668, 59755, 70667, 84626, 99795, 118991
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OFFSET
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0,6
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COMMENTS
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Also, a(n) gives the number of partitions of 2*n in which all parts are even and less than n.
Also, number of nonpalindromic partitions of n, n >= 1. In other words: a(n) is the number of partitions of n into parts which cannot be listed in palindromic order, n >= 1. - Omar E. Pol, Jan 11 2014
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LINKS
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FORMULA
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EXAMPLE
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a(7) = 8, because 3+3+1 = 3+2+2 = 3+2+1+1 = 3+1+1+1+1 = 2+2+2+1 = 2+2+1+1+1 = 2+1+1+1+1+1 = 1+1+1+1+1+1+1, exhausting the partitions of the indicated class for n=7.
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MAPLE
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b:= proc(n, i) option remember;
if n=0 then 1
elif i<1 then 0
else b(n, i-1) +`if`(i>n, 0, b(n-i, i))
fi
end:
a:= n-> b(n, ceil(n/2)-1):
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MATHEMATICA
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b[n_, i_] := b[n, i] = If[n==0, 1, If[i<1, 0, b[n, i-1] + If[i>n, 0, b[n-i, i]]]]; a[n_] := b[n, Ceiling[n/2]-1]; Table[a[n], {n, 0, 50}] (* Jean-François Alcover, Jan 09 2016, after Alois P. Heinz *)
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CROSSREFS
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Row sums of triangle A124278, for n >= 3.
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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