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A308159 Sum of the largest sides of all integer-sided isosceles triangles with perimeter n. 1
0, 0, 1, 0, 2, 2, 6, 3, 7, 8, 14, 9, 16, 17, 25, 19, 28, 29, 40, 32, 43, 45, 58, 48, 62, 64, 79, 68, 84, 86, 104, 91, 109, 112, 132, 117, 138, 141, 163, 147, 170, 173, 198, 180, 205, 209, 236, 216, 244, 248, 277, 256, 286, 290, 322, 299, 331, 336, 370, 345 (list; graph; refs; listen; history; text; internal format)
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]) * (n-i-k), where [] is the Iverson bracket.

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

G.f.: x^3*(1 + 2*x^2 + x^3 + 4*x^4 + x^5 + x^6) / ((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[(n - i - 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. A308158.

Sequence in context: A028421 A263003 A344469 * A081745 A240578 A273105

Adjacent sequences:  A308156 A308157 A308158 * A308160 A308161 A308162

KEYWORD

nonn

AUTHOR

Wesley Ivan Hurt, May 14 2019

STATUS

approved

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Last modified September 23 19:03 EDT 2021. Contains 347617 sequences. (Running on oeis4.)