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 A100471 Number of partitions whose sequence of frequencies is increasing. 3
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..1000 EXAMPLE 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. 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=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 PROG (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 CROSSREFS Cf. A100881, A100882, A100883. Cf. A098859. Sequence in context: A208963 A011142 A060029 * A095700 A035944 A050366 Adjacent sequences:  A100468 A100469 A100470 * A100472 A100473 A100474 KEYWORD nonn,changed AUTHOR David S. Newman, Nov 21 2004 EXTENSIONS Corrected and extended by Vladeta Jovovic, Nov 24 2004 STATUS approved

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