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URL: https://oeis.org/A308158

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A308158
Sum of the smallest side lengths of all integer-sided isosceles triangles with perimeter n.
2
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
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: A350840 A385574 A176789 * A325349 A320054 A215228
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, May 14 2019
STATUS
approved