A096740 Number of partitions of n into distinct parts >= 11.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 9, 10, 11, 13, 14, 16, 18, 20, 22, 25, 27, 30, 33, 36, 40, 44, 48, 53, 59, 64, 71, 78, 86, 94, 104, 113, 125, 136, 149, 163, 179, 194, 213, 232, 254, 276, 302, 328, 359, 390, 425

Offset

0,24

Comments

The old entry with this sequence number was a duplicate of A071569.

Links

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

Formula

a(n) = A026831(n+10). - R. J. Mathar, Jul 31 2008

G.f.: Product_{j>=11} (1+x^j). - R. J. Mathar, Jul 31 2008

G.f.: Sum_{k>=0} x^(k*(k + 21)/2) / Product_{j=1..k} (1 - x^j). - Ilya Gutkovskiy, Nov 24 2020

Maple

b:= proc(n, i) option remember;
      `if`(n=0, 1, `if`((i-10)*(i+11)/2<n, 0,
       add(b(n-i*j, i-1), j=0..min(1, n/i))))
    end:
a:= n-> b(n$2):
seq(a(n), n=0..100);  # Alois P. Heinz, Feb 07 2014

Mathematica

d[n_] := Select[IntegerPartitions[n], Max[Length /@ Split@#] == 1 && Min[#] >= 11 &]; Table[d[n], {n, 30}] (* str partitions, parts >= 11 *)
Table[Length[d[n]], {n, 40}] (* A096740 for n >= 1 *)
(* Clark Kimberling, Mar 07 2014 *)
b[n_, i_] := b[n, i] = If[n == 0, 1, If[(i-10)*(i+11)/2 < n, 0, Sum[b[n - i*j, i-1], {j, 0, Min[1, n/i]}]]]; a[n_] := b[n, n]; Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Nov 11 2015, after Alois P. Heinz *)

Crossrefs

Cf. A025147.

Sequence in context: A021895 A025160 A026831 * A264595 A026830 A025155

Adjacent sequences: A096737 A096738 A096739 * A096741 A096742 A096743

Keyword

nonn

Author

N. J. A. Sloane, Sep 28 2008

Status

approved