A308452 Number of integer-sided triangles with perimeter n and side lengths a, b and c such that a <= b <= c, and b is prime.

0, 0, 0, 0, 1, 1, 2, 1, 2, 1, 2, 1, 2, 2, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 5, 4, 6, 6, 8, 8, 10, 9, 11, 10, 12, 11, 14, 12, 14, 12, 14, 12, 14, 13, 16, 15, 18, 17, 20, 18, 20, 19, 21, 20, 22, 20, 22, 20, 22, 20, 23, 21, 24, 22, 25, 23, 26, 24, 26, 24, 26

Offset

1,7

Links

Table of n, a(n) for n=1..73.

Wikipedia, Integer Triangle

Formula

a(n) = Sum_{k=1..floor(n/3)} Sum_{i=k..floor((n-k)/2)} sign(floor((i+k)/(n-i-k+1))) * A010051(i).

Mathematica

Table[Sum[Sum[ (PrimePi[i] - PrimePi[i - 1]) Sign[Floor[(i + k)/(n - i - k + 1)]], {i, k, Floor[(n - k)/2]}], {k, Floor[n/3]}], {n, 100}]

Crossrefs

Cf. A010051, A308451.

Sequence in context: A161260 A161285 A235189 * A103682 A023134 A304536

Adjacent sequences: A308449 A308450 A308451 * A308453 A308454 A308455

Keyword

nonn

Author

Wesley Ivan Hurt, May 27 2019

Status

approved