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A307857
Number of partitions of n into 1, 2 or 3 nonprime parts.
4
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
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
KEYWORD
nonn,easy
AUTHOR
Wesley Ivan Hurt, May 01 2019
STATUS
approved