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A305717 Number of distinct Heronian triangles with perimeter A051518(n). 10
1, 1, 1, 1, 1, 2, 4, 1, 2, 1, 3, 2, 4, 1, 3, 5, 1, 1, 2, 5, 1, 1, 4, 8, 1, 5, 5, 6, 5, 2, 12, 1, 6, 1, 5, 4, 9, 1, 9, 2, 5, 11, 8, 2, 3, 5, 7, 12, 1, 10, 1, 1, 1, 7, 10, 3, 2, 2, 15, 14, 5, 10, 5, 5, 11, 16, 5, 1, 12, 7, 3, 1, 7, 1, 2, 15, 16, 1, 11, 16, 18 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,6
LINKS
FORMULA
a(n) = A051516(A051518(n)).
EXAMPLE
For n = 7, the a(7) = 4 Heronian triangles with perimeter A051518(7) = 36 are:
the 10-13-13 isosceles triangle (area 60),
the 10-10-16 isosceles triangle (area 48),
the 9-12-15 scalene triangle (area 54), and
the 9-10-17 scalene triangle (area 36).
MATHEMATICA
htc[p_] := Block[{t=0, c, q=p/2}, Do[c=p-a-b; If[c >= b && a+c > b && a+b > c && IntegerQ[Sqrt[q (q-a) (q-b) (q-c)]], t++], {a, p/3}, {b, a, p-a-1}]; t]; Select[htc /@ (Range[128] 2), # > 0 &] (* Giovanni Resta, Jun 14 2018 *)
CROSSREFS
Sequence in context: A030420 A133902 A265823 * A208645 A361381 A054708
KEYWORD
nonn
AUTHOR
Peter Kagey, Jun 08 2018
STATUS
approved

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Last modified May 25 05:18 EDT 2024. Contains 372782 sequences. (Running on oeis4.)