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A025151 Number of partitions of n into distinct parts >= 6. 3
1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 7, 7, 9, 10, 12, 13, 16, 17, 20, 23, 26, 29, 34, 38, 43, 49, 55, 62, 70, 79, 88, 100, 111, 125, 140, 157, 174, 196, 217, 243, 270, 301, 333, 372, 411, 457, 506, 561, 619, 687, 757, 837, 924, 1019, 1122, 1238, 1361, 1498 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,14

LINKS

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

FORMULA

a(n) = A026826(n+5). - R. J. Mathar, Jul 31 2008

G.f.: product_{j=6..infinity} (1+x^j). - R. J. Mathar, Jul 31 2008

MAPLE

b:= proc(n, i) option remember;

      `if`(n=0, 1, `if`((i-5)*(i+6)/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[#] >= 6 &]; Table[d[n], {n, 16}] (* strict partitions, parts >= 6 *)

Table[Length[d[n]], {n, 40}] (* A025151 for n >= 1 *)

(* Clark Kimberling, Mar 07 2014 *)

b[n_, i_] := b[n, i] = If[n == 0, 1, If[(i - 5)(i + 6)/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-Fran├žois Alcover, Aug 29 2016, after Alois P. Heinz *)

CROSSREFS

Cf. A025147.

Sequence in context: A237979 A264591 A026826 * A026801 A185328 A210718

Adjacent sequences:  A025148 A025149 A025150 * A025152 A025153 A025154

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling

STATUS

approved

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Last modified September 26 06:54 EDT 2017. Contains 292502 sequences.