A026828 Number of partitions of n into distinct parts, the least being 7.

0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 8, 8, 10, 11, 13, 14, 17, 18, 21, 23, 26, 29, 33, 36, 41, 46, 51, 57, 64, 71, 79, 88, 97, 109, 120, 133, 147, 164, 180, 200, 220, 244, 268, 297, 325, 360, 395, 435, 477, 526, 575, 633, 693

Offset

0,25

Links

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

Formula

a(n) = A025153(n-7), n>7. - R. J. Mathar, Jul 31 2008

G.f.: x^7*Product_{j>=8} (1+x^j). - R. J. Mathar, Jul 31 2008

G.f.: Sum_{k>=1} x^(k*(k + 13)/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-7)*(i+8)/2<n, 0,
       add(b(n-i*j, i-1), j=0..min(1, n/i))))
    end:
a:= n-> `if`(n<7, 0, b(n-7$2)):
seq(a(n), n=0..100);  # Alois P. Heinz, Feb 07 2014

Mathematica

b[n_, i_] := b[n, i] = If[n == 0, 1, If[(i-7)*(i+8)/2 < n, 0, Sum[b[n - i*j, i - 1], {j, 0, Min[1, n/i]}]]]; a[n_] := If[n < 7, 0, b[n-7, n-7]]; Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Jun 24 2015, after Alois P. Heinz *)
Join[{0}, Table[Count[ Last /@ Select[IntegerPartitions@n, DeleteDuplicates[#] == # &], 7], {n, 66}]] (* Robert Price, Jun 13 2020 *)

Crossrefs

Cf. A025147, A025153.

Sequence in context: A241827 A096401 A264593 * A025153 A026803 A286041

Adjacent sequences: A026825 A026826 A026827 * A026829 A026830 A026831

Keyword

nonn

Author

Clark Kimberling

Status

approved