login
A308069
Number of integer-sided triangles with perimeter n whose side lengths are semiprime.
1
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 2, 1, 2, 1, 1, 1, 1, 2, 2, 1, 2, 3, 4, 2, 1, 1, 2, 2, 1, 0, 1, 1, 2, 4, 4, 2, 2, 2, 3, 4, 4, 5, 5, 4, 7, 6, 4, 2, 3, 5, 4, 2, 2, 3, 3, 3, 5, 8, 6, 6, 7, 7, 8, 7, 7, 10, 9, 9, 10, 12, 14, 10, 7, 9
OFFSET
1,22
FORMULA
a(n) = Sum_{k=1..floor(n/3)} Sum_{i=k..floor((n-k)/2)} sign(floor((i+k)/(n-i-k+1))) * c(i) * c(k) * c(n-i-k), where c is the semiprime characteristic (A064911).
MATHEMATICA
Table[Sum[Sum[KroneckerDelta[PrimeOmega[i], 2] KroneckerDelta[PrimeOmega[k], 2] KroneckerDelta[PrimeOmega[n - i - k], 2]*Sign[Floor[(i + k)/(n - i - k + 1)]], {i, k, Floor[(n - k)/2]}], {k, Floor[n/3]}], {n, 100}]
CROSSREFS
Cf. A064911.
Sequence in context: A337277 A269974 A269975 * A161895 A048138 A165022
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, May 10 2019
STATUS
approved