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A338896 Inradii of Pythagorean triples of A338895. 2
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 (list; table; graph; refs; listen; history; text; internal format)
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).

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

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Last modified August 3 07:58 EDT 2021. Contains 346435 sequences. (Running on oeis4.)