A307857 Number of partitions of n into 1, 2 or 3 nonprime parts.

1, 1, 1, 1, 1, 2, 1, 3, 3, 4, 3, 5, 4, 6, 5, 9, 7, 10, 8, 12, 10, 15, 11, 18, 15, 20, 17, 24, 19, 28, 22, 30, 26, 36, 29, 41, 34, 42, 37, 51, 41, 55, 47, 59, 53, 66, 54, 73, 63, 78, 70, 85, 72, 94, 81, 99, 89, 108, 92, 118, 102, 121, 110, 135, 117, 143, 126

Offset

1,6

Links

Table of n, a(n) for n=1..67.

Index entries for sequences related to partitions

Formula

a(n) = c(n) + ( Sum_{i=1..floor(n/2)} c(i) * c(n-i) ) + ( Sum_{j=1..floor(n/3)} Sum_{i=j..floor(n-j)/2)} c(i) * c(j) * c(n-i-j) ), where c = A005171.

Example

a(9) = 3, because 9 can be written as the sum of nonprimes with at most 3 parts in three ways: 9 = 8+1 = 4+4+1.
a(10) = 4, because 10 can be written as the sum of nonprimes with at most 3 parts in four ways: 10 = 9+1 = 6+4 = 8+1+1.
a(11) = 3, because 11 can be written as the sum of nonprimes with at most 3 parts in three ways: 10+1 = 9+1+1 = 6+4+1.
a(12) = 5, because 12 can be written as the sum of nonprimes with at most 3 parts in five ways: 12 = 8+4 = 6+6 = 10+1+1 = 4+4+4.

Crossrefs

Cf. A005171, A018252, A071335.

Sequence in context: A116087 A328518 A163281 * A116921 A173989 A093068

Adjacent sequences: A307854 A307855 A307856 * A307858 A307859 A307860

Keyword

nonn,easy

Author

Wesley Ivan Hurt, May 01 2019

Status

approved