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A308102 Sum of the perimeters of all integer-sided scalene triangles with perimeter n. 0
0, 0, 0, 0, 0, 0, 0, 0, 9, 0, 11, 12, 26, 14, 45, 32, 68, 54, 95, 80, 147, 110, 184, 168, 250, 208, 324, 280, 406, 360, 496, 448, 627, 544, 735, 684, 888, 798, 1053, 960, 1230, 1134, 1419, 1320, 1665, 1518, 1880, 1776, 2156, 2000, 2448, 2288, 2756, 2592 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,9

LINKS

Table of n, a(n) for n=1..54.

Wikipedia, Integer Triangle

FORMULA

a(n) = n * Sum_{k=1..floor((n-1)/3)} Sum_{i=k+1..floor((n-k-1)/2)} sign(floor((i+k)/(n-i-k+1))).

Conjectures from Colin Barker, May 13 2019: (Start)

G.f.: x^9*(3 + 2*x + x^2)*(3 + x + 2*x^2) / ((1 - x)^4*(1 + x)^3*(1 + x^2)^2*(1 + x + x^2)^2).

a(n) = -a(n-1) + 2*a(n-3) + 4*a(n-4) + 2*a(n-5) - a(n-6) - 5*a(n-7) - 5*a(n-8) - a(n-9) + 2*a(n-10) + 4*a(n-11) + 2*a(n-12) - a(n-14) - a(n-15) for n>15.

(End)

MATHEMATICA

Table[n*Sum[Sum[Sign[Floor[(i + k)/(n - i - k + 1)]], {i, k + 1,

Floor[(n - k - 1)/2]}], {k, Floor[(n - 1)/3]}], {n, 100}]

PROG

(PARI) a(n) = n * sum(k=1, (n-1)\3, sum(i=k+1, (n-k-1)\2, sign((i+k)\(n-i-k+1)))); \\ Michel Marcus, May 13 2019

CROSSREFS

Cf. A005044.

Sequence in context: A056965 A341486 A320379 * A338016 A062047 A117465

Adjacent sequences:  A308099 A308100 A308101 * A308103 A308104 A308105

KEYWORD

nonn

AUTHOR

Wesley Ivan Hurt, May 12 2019

STATUS

approved

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Last modified August 3 17:13 EDT 2021. Contains 346439 sequences. (Running on oeis4.)