A307966 Sum of the largest side lengths of all integer-sided triangles with perimeter n.

0, 0, 1, 0, 2, 2, 6, 3, 11, 8, 19, 14, 28, 23, 45, 33, 59, 52, 83, 67, 109, 93, 141, 121, 175, 155, 224, 191, 267, 243, 327, 288, 390, 351, 462, 417, 537, 492, 634, 570, 722, 671, 834, 762, 950, 878, 1078, 998, 1210, 1130, 1371, 1266, 1520, 1432, 1700, 1585

Offset

1,5

Links

Table of n, a(n) for n=1..56.

Formula

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

Conjectures from Colin Barker, May 12 2019: (Start)

G.f.: x^3*(1 + x + 2*x^2 + 2*x^3 + 4*x^4 + 3*x^5 + 3*x^6) / ((1 - x)^4*(1 + x)^3*(1 + x^2)^2*(1 + x + x^2)^2).

a(n) = -a(n-1) + 2*a(n-3) + 4*a(n-4) + 2*a(n-5) - a(n-6) - 5*a(n-7) - 5*a(n-8) - a(n-9) + 2*a(n-10) + 4*a(n-11) + 2*a(n-12) - a(n-14) - a(n-15) for n>15.

(End)

Mathematica

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

Prog

(PARI) a(n) = sum(k=1, n\3, sum(i=k, (n-k)\2, sign((i+k)\(n-i-k+1)) * (n-i-k))); \\ Michel Marcus, May 13 2019

Crossrefs

Cf. A005044.

Sequence in context: A240578 A273105 A370370 * A129889 A263673 A304987

Adjacent sequences: A307963 A307964 A307965 * A307967 A307968 A307969

Keyword

nonn

Author

Wesley Ivan Hurt, May 11 2019

Status

approved