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 A330912 Sum of the smallest side lengths of all Heronian triangles with perimeter A051518(n). 7
 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

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Last modified March 1 08:46 EST 2024. Contains 370430 sequences. (Running on oeis4.)