A338896 Inradii of Pythagorean triples of A338895.

0, 2, 0, 4, 4, 0, 6, 8, 6, 0, 8, 12, 12, 8, 0, 10, 16, 18, 16, 10, 0, 12, 20, 24, 24, 20, 12, 0, 14, 24, 30, 32, 30, 24, 14, 0, 16, 28, 36, 40, 40, 36, 28, 16, 0, 18, 32, 42, 48, 50, 48, 42, 32, 18, 0, 20, 36, 48, 56, 60, 60, 56, 48, 36, 20, 0

Offset

1,2

Comments

Without the 0's, the sequence becomes 2*A003991. The 0 indices are triangular numbers A000217.

Links

Table of n, a(n) for n=1..66.

Ron Knott, Pythagorean Triples and Online Calculators

Formula

When m and n define a row of triples in A338275 that gives rise to a triple (a row) of A338895, the current term corresponding to such a row is (m-n-1)*n/2.

If [a,b,c] is the n-th row of A338895, then a(n) = a*b/(a+b+c).

T(n, k) = 2*k*(n - k). Follows from the first comment. - Peter Luschny, Apr 17 2023

Example

m 3
n 2  [0,4,4]    0
------------------
m 5
n 2  [6,8,10]   2
n 4  [0,16,16]  0
------------------
m 7
n 2  [16,12,20] 4
n 4  [10,24,26] 4
n 6  [0,36,36]  0
------------------
m 9
n 2  [30,16,34] 6
n 4  [24,32,40] 8
n 6  [14,48,50] 6
n 8  [0,64,64]  0
------------------.
The 7th row of A338895 is [30,16,34], so a(7) = 30*16/(30+16+34) = 6.
As a triangle:
   0
   2, 0
   4, 4, 0
   6, 8, 6, 0
   8, 12, 12, 8, 0
  10, 16, 18, 16, 10, 0
  12, 20, 24, 24, 20, 12, 0,

Mathematica

Table[#1 #2/Total[{##}] & @@ {((#1 - 1)^2 - #2^2)/2, (#1 - 1) #2, ((#1 - 1)^2 + #2^2)/2} & @@ {m, n}, {m, 3, 23, 2}, {n, 2, m, 2}] // Flatten (* Michael De Vlieger, Dec 04 2020 *)

Prog

(PARI) lista(mm) = forstep (m=3, mm, 2, forstep (n=2, m, 2, my(v=[((m-1)^2 - n^2)/2, (m-1)*n, ((m-1)^2 + n^2)/2]); print1(v[1]*v[2]/vecsum(v), ", "))); \\ Michel Marcus, Dec 04 2020

Crossrefs

Cf. A338275, A338895.

Cf. A003991 (see 2nd comment).

Sequence in context: A307658 A265511 A081236 * A182059 A103328 A344563

Adjacent sequences: A338893 A338894 A338895 * A338897 A338898 A338899

Keyword

nonn,tabl

Author

David Lovler, Nov 14 2020

Status

approved