A330912 - OEIS

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A330912

Sum of the smallest side lengths of all Heronian triangles with perimeter A051518(n).

3, 5, 5, 6, 5, 14, 38, 8, 20, 11, 37, 29, 43, 7, 31, 64, 11, 17, 37, 84, 19, 15, 70, 130, 22, 87, 101, 133, 122, 38, 241, 25, 149, 25, 111, 123, 225, 39, 220, 54, 120, 327, 254, 57, 103, 162, 227, 371, 41, 321, 34, 43, 29, 278, 373, 76, 70, 95, 577, 567, 157, 476, 221

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

Table of n, a(n) for n=1..63.

Eric Weisstein's World of Mathematics, Heronian Triangle

Wikipedia, Heronian triangle

Wikipedia, Integer Triangle

FORMULA

a(n) = Sum_{k=1..floor(c(n)/3)} Sum_{i=k..floor((c(n)-k)/2)} sign(floor((i+k)/(c(n)-i-k+1))) * chi(sqrt((c(n)/2)*(c(n)/2-i)*(c(n)/2-k)*(c(n)/2-(c(n)-i-k)))) * k, where chi(n) = 1 - ceiling(n) + floor(n) and c(n) = A051518(n). - Wesley Ivan Hurt, May 12 2020

EXAMPLE

a(1) = 3; there is one Heronian triangle with perimeter A051518(1) = 12, which is [3,4,5] and its smallest side length is 3.

a(6) = 14; there are two Heronian triangles with perimeter A051518(6) = 32, [4,13,15] and [10,10,12]. The sum is 4 + 10 = 14.

CROSSREFS

Cf. A051516, A051518, A070138, A096468, A298079, A298614, A305717.

Cf. A330915, A330916.

Sequence in context: A258714 A143082 A330917 * A029912 A272756 A322350

Adjacent sequences: A330909 A330910 A330911 * A330913 A330914 A330915

KEYWORD

nonn

AUTHOR

Wesley Ivan Hurt, May 02 2020

STATUS

approved