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A100471
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Number of partitions whose sequence of frequencies is increasing.
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3
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1, 1, 2, 2, 4, 4, 7, 8, 11, 13, 18, 20, 27, 32, 40, 44, 60, 67, 82, 93, 114, 129, 161, 175, 209, 239, 285, 315, 372, 416, 484, 545, 631, 698, 811, 890, 1027, 1146, 1304, 1437, 1631, 1805, 2042, 2252, 2539, 2785, 3143, 3439, 3846, 4226, 4722, 5159
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history;
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OFFSET
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0,3
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 0..1000
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EXAMPLE
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a(4) = 4 because of the 5 unrestricted partitions of 4, only one, 3+1 uses each of its summands just once and 1,1 is not an increasing sequence.
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MAPLE
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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=t+1..floor(n/i))
fi
end:
a:= n-> b(n, n, 0):
seq (a(n), n=0..60); # Alois P. Heinz, Feb 21 2011
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PROG
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(Haskell)
a100471 n = p 0 (n + 1) 1 n where
p m m' k x | x == 0 = if m < m' || m == 0 then 1 else 0
| x < k = 0
| m == 0 = p 1 m' k (x - k) + p 0 m' (k + 1) x
| otherwise = p (m + 1) m' k (x - k) +
if m < m' then p 0 m (k + 1) x else 0
-- Reinhard Zumkeller, Dec 27 2012
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CROSSREFS
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Cf. A100881, A100882, A100883.
Cf. A098859.
Sequence in context: A208963 A011142 A060029 * A095700 A035944 A050366
Adjacent sequences: A100468 A100469 A100470 * A100472 A100473 A100474
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KEYWORD
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nonn,changed
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AUTHOR
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David S. Newman, Nov 21 2004
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EXTENSIONS
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Corrected and extended by Vladeta Jovovic, Nov 24 2004
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STATUS
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approved
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