OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..1000
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