A100882 Number of partitions of n in which the sequence of frequencies of the summands is nonincreasing.

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

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

Cf. A100881, A100883, A100884.

Sequence in context: A331076 A316496 A332339 * A171979 A361858 A181694

Adjacent sequences: A100879 A100880 A100881 * A100883 A100884 A100885

Keyword

nonn

Author

David S. Newman, Nov 21 2004

Extensions

More terms from Alois P. Heinz, Feb 21 2011

Status

approved