A318604 Number of partitions of prime(n) into distinct parts not larger than prime(n-1).

1, 1, 3, 7, 16, 33, 52, 99, 246, 338, 750, 1255, 1608, 2585, 5110, 9782, 12074, 22240, 32987, 40024, 70478, 101693, 173672, 345837, 483325, 570076, 789635, 927404, 1274113, 3725322, 5010683, 7755766, 8953854, 18108385, 20792118, 31316304, 46828022, 61000699

Offset

2,3

Comments

The first prime number taken into consideration in the sequence is prime(2)=3, as 2 does not have a preceding prime.

Links

Alois P. Heinz, Table of n, a(n) for n = 2..1000

Example

a(5) = 7: there are 7 partitions of prime(5) = 11 into distinct parts not larger than prime(4) = 7: [7,4], [7,3,1], [6,5], [6,4,1], [6,3,2], [5,4,2], [5,3,2,1].

Maple

b:= proc(n, i) option remember; (m-> `if`(m<n, 0, `if`(m=n, 1,
      b(n, i-1)+b(n-i, min(n-i, i-1)))))(i*(i+1)/2)
    end:
a:= n-> (p-> b(p(n), p(n-1)))(ithprime):
seq(a(n), n=2..50);  # Alois P. Heinz, Aug 29 2018

Mathematica

b[n_, i_] := b[n, i] = Function[m, If[m < n, 0, If[m == n, 1, b[n, i - 1] + b[n - i, Min[n - i, i - 1]]]]][i(i+1)/2];
a[n_] := b[Prime[n], Prime[n - 1]];
a /@ Range[2, 50] (* Jean-François Alcover, Nov 30 2020, after Alois P. Heinz *)

Crossrefs

Sequence in context: A298311 A366527 A161810 * A084631 A219846 A229914

Adjacent sequences: A318601 A318602 A318603 * A318605 A318606 A318607

Keyword

nonn

Author

Pierandrea Formusa, Aug 29 2018

Extensions

a(26)-a(39) from Alois P. Heinz, Aug 29 2018

Status

approved