A308158 Sum of the smallest side lengths of all integer-sided isosceles triangles with perimeter n.

0, 0, 1, 0, 1, 2, 3, 2, 4, 5, 7, 6, 8, 10, 13, 11, 14, 17, 20, 18, 22, 25, 29, 27, 31, 35, 40, 37, 42, 47, 52, 49, 55, 60, 66, 63, 69, 75, 82, 78, 85, 92, 99, 95, 103, 110, 118, 114, 122, 130, 139, 134, 143, 152, 161, 156, 166, 175, 185, 180, 190, 200, 211

Offset

1,6

Links

Table of n, a(n) for n=1..63.

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))) * ([i=k] + [i=n-i-k] - [k=n-i-k]) * k, where [] is the Iverson bracket.

Conjectures from Colin Barker, May 15 2019: (Start)

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

a(n) = a(n-3) + 2*a(n-4) - 2*a(n-7) - a(n-8) + a(n-11) for n>11.

(End)

Mathematica

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

Crossrefs

Cf. A059169.

Sequence in context: A365384 A350840 A176789 * A325349 A320054 A215228

Adjacent sequences: A308155 A308156 A308157 * A308159 A308160 A308161

Keyword

nonn

Author

Wesley Ivan Hurt, May 14 2019

Status

approved