VOOZH about

URL: https://oeis.org/A308160

⇱ A308160 - OEIS

login
A308160
Take all the integer-sided isosceles triangles with perimeter n and sides a, b, and c such that a <= b <= c. a(n) is the sum of all the b's.
0
0, 0, 1, 0, 2, 2, 5, 3, 7, 7, 12, 9, 15, 15, 22, 18, 26, 26, 35, 30, 40, 40, 51, 45, 57, 57, 70, 63, 77, 77, 92, 84, 100, 100, 117, 108, 126, 126, 145, 135, 155, 155, 176, 165, 187, 187, 210, 198, 222, 222, 247, 234, 260, 260, 287, 273, 301, 301, 330, 315
OFFSET
1,5
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]) * i, where [] is the Iverson bracket.
Conjectures from Colin Barker, May 15 2019: (Start)
G.f.: x^3*(1 - x + 2*x^2 + x^4) / ((1 - x)^3*(1 + x)^2*(1 + x^2)^2).
a(n) = a(n-1) + 2*a(n-4) - 2*a(n-5) - a(n-8) + a(n-9) for n>9.
(End)
MATHEMATICA
Table[Sum[Sum[i (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
Sequence in context: A178179 A284833 A321202 * A151729 A088652 A368207
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, May 14 2019
STATUS
approved