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A100882
Number of partitions of n in which the sequence of frequencies of the summands is nonincreasing.
21
1, 1, 2, 3, 4, 5, 8, 8, 12, 14, 18, 21, 29, 29, 40, 47, 56, 62, 83, 86, 111, 124, 146, 166, 207, 217, 267, 300, 352, 389, 471, 505, 604, 668, 772, 860, 1015, 1085, 1279, 1419, 1622, 1780, 2072, 2242, 2595, 2858, 3231, 3563, 4092, 4421, 5057, 5557, 6250
OFFSET
0,3
LINKS
EXAMPLE
a(4) = 4 because in each of the partitions 4, 3+1, 2+2, 1+1+1+1, the frequencies of the summands is nonincreasing as the summands decrease. The partition 2+1+1 is not counted because 2 is used once, but 1 is used twice.
MAPLE
b:= proc(n, i, t) option remember;
if n<0 then 0
elif n=0 then 1
elif i=1 then `if`(n<=t, 1, 0)
elif i=0 then 0
else b(n, i-1, t)
+add(b(n-i*j, i-1, j), j=1..min(t, floor(n/i)))
fi
end:
a:= n-> b(n, n, n):
seq(a(n), n=0..60); # Alois P. Heinz, Feb 21 2011
MATHEMATICA
b[n_, i_, t_] := b[n, i, t] = Which[n<0, 0, n == 0, 1, i == 1, If[n <= t, 1, 0], i == 0, 0, True, b[n, i-1, t] + Sum[b[n-i*j, i-1, j], {j, 1, Min[t, Floor[n/i]]}]]; a[n_] := b[n, n, n]; Table[a[n], {n, 0, 60}] (* Jean-François Alcover, Oct 26 2015, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
David S. Newman, Nov 21 2004
EXTENSIONS
More terms from Alois P. Heinz, Feb 21 2011
STATUS
approved