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, 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

Links

Table of n, a(n) for n=1..60.

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]) * 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

Cf. A308158, A308159.

Sequence in context: A178179 A284833 A321202 * A151729 A088652 A368207

Adjacent sequences: A308157 A308158 A308159 * A308161 A308162 A308163

Keyword

nonn

Author

Wesley Ivan Hurt, May 14 2019

Status

approved