A026825 Number of partitions of n into distinct parts, the least being 4.

0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 3, 3, 4, 4, 5, 6, 7, 8, 10, 11, 13, 15, 17, 20, 23, 26, 30, 35, 39, 45, 51, 58, 66, 75, 84, 96, 108, 122, 137, 155, 173, 195, 219, 245, 274, 307, 342, 383, 427, 475, 529, 589, 654, 727, 807, 894, 991, 1098, 1214, 1343, 1485, 1638, 1809

Offset

0,16

Links

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

Formula

a(n) = A025150(n-4), n>4. - R. J. Mathar, Jul 31 2008

G.f.: x^4*Product_{j>=5} (1+x^j). - R. J. Mathar, Jul 31 2008

G.f.: Sum_{k>=1} x^(k*(k + 7)/2) / Product_{j=1..k-1} (1 - x^j). - Ilya Gutkovskiy, Nov 24 2020

Maple

b:= proc(n, i) option remember;
      `if`(n=0, 1, `if`((i-4)*(i+5)/2<n, 0,
       add(b(n-i*j, i-1), j=0..min(1, n/i))))
    end:
a:= n-> `if`(n<4, 0, b(n-4$2)):
seq(a(n), n=0..80);  # Alois P. Heinz, Feb 07 2014

Mathematica

b[n_, i_] := b[n, i] = If[n == 0, 1, If[(i-4)*(i+5)/2 < n, 0, Sum[b[n-i*j, i-1], {j, 0, Min[1, n/i]}]]]; a[n_] := If[n<4, 0, b[n-4, n-4]]; Table[a[n], {n, 0, 80}] (* Jean-François Alcover, Jun 24 2015, after Alois P. Heinz *)
Join[{0}, Table[Count[Last /@ Select[IntegerPartitions@n, DeleteDuplicates[#] == # &], 4], {n, 66}]] (* Robert Price, Jun 13 2020 *)

Crossrefs

Cf. A025147, A025150.

Sequence in context: A025157 A006141 A185229 * A025150 A026800 A185327

Adjacent sequences: A026822 A026823 A026824 * A026826 A026827 A026828

Keyword

nonn

Author

Clark Kimberling

Status

approved