A316844 -id:A316844 - cp's OEIS frontend

A317181 Consider primitive integer triangles as listed in rows of table A316842. Sequence gives 16*area^2 for these triangles in the same order.

3, 15, 63, 35, 128, 135, 320, 63, 495, 275, 231, 576, 975, 99, 384, 819, 1344, 455, 351, 896, 1575, 2304, 143, 2975, 735, 675, 1536, 2499, 495, 1280, 2295, 3456, 4655, 195, 768, 1683, 2880, 4275, 5760, 1071, 2304, 935, 3591, 663, 1728, 3135, 4800, 6615, 8448, 255, 2223, 5775, 10143

Offset: 1

N. J. A. Sloane, Jul 23 2018

Lars Blomberg, Table of n, a(n) for n = 1..3000

Cf. A316842, A316852, A316846, A316847, A316848.

Subsequence of A316853.

a(n) = 16*s*(s-a)*(s-b)*(s-c) where s = A316852(n)/2, and a,b,c are A316843(n), A316844(n), A316845(n).

A331257 Numerator of squared radius of inscribed circle of the n-th triangle with integer sides in the list given by A316841. Denominators are A331258.

Original entry on oeis.org

1, 3, 1, 9, 5, 1, 3, 5, 4, 7, 3, 45, 4, 25, 21, 1, 75, 9, 2, 63, 12, 25, 35, 9, 27, 8, 7, 9, 11, 5, 27, 2, 175, 3, 49, 3, 3, 147, 11, 5, 135, 8, 245, 13, 3, 99, 20, 225, 18, 49, 63, 16, 55, 5, 189, 16, 39, 4, 165, 3, 15, 48, 15, 7, 117, 12, 275, 45, 441, 16

Offset: 1

Hugo Pfoertner, Jan 26 2020

			   n i (A316843)
   | | j (A316844)
   | | | k (A316845)
   | | | |  a(n) this sequence
   | | | |  |  A331258(n)
   | | | |  |  |  rho = sqrt(a(n)/A331258(n))
   1 1 1 1  1 12  0.28868
   2 2 2 1  3 20  0.38730
   3 2 2 2  1  3  0.57735
   4 3 2 2  9 28  0.56695
   5 3 3 1  5 28  0.42258
   6 3 3 2  1  2  0.70711
   7 3 3 3  3  4  0.86603
   8 4 3 2  5 12  0.64550
   9 4 3 3  4  5  0.89443
  10 4 4 1  7 36  0.44096
  11 4 4 2  3  5  0.77460
  12 4 4 3 45 44  1.01130
  13 4 4 4  4  3  1.15470
  14 5 3 3 25 44  0.75378
  15 5 4 2 21 44  0.69085
  16 5 4 3  1  1  1.00000

Cf. A316841, A316843, A316844, A316845, A331258.

rh2(a, b, c)={my(s=(a+b+c)/2); (s-a)*(s-b)*(s-c)/s};
for(i=1, 8, for(j=1, i, for(k=1, j, if(j+k>i, print1(numerator(rh2(i, j, k)), ", ")))))

Radius of inscribed circle of a triangle with sides (a,b,c):

rho(a,b,c) = sqrt((s - a)*(s - b)*(s - c)/s) with s = (a + b + c)/2.

A331258 Denominator of squared radius of inscribed circle of the n-th triangle with integer sides in the list given by A316841. Numerators are A331257.

Original entry on oeis.org

12, 20, 3, 28, 28, 2, 4, 12, 5, 36, 5, 44, 3, 44, 44, 1, 52, 44, 3, 52, 7, 12, 52, 7, 52, 7, 4, 4, 52, 7, 20, 1, 68, 1, 60, 4, 2, 68, 20, 4, 68, 3, 76, 60, 4, 68, 9, 76, 5, 12, 68, 9, 68, 3, 76, 5, 68, 3, 76, 1, 4, 11, 68, 9, 76, 5, 84, 11, 92, 3, 76, 76, 1

Offset: 1

Hugo Pfoertner, Jan 26 2020

			See A331257.

Cf. A316841, A316843, A316844, A316845, A331257.

rh2(a,b,c)={my(s=(a+b+c)/2); (s-a)*(s-b)*(s-c)/s};
for(i=1,8, for(j=1,i, for(k=1,j, if(j+k>i, print1(denominator(rh2(i,j,k)),", ")))))

cp's OEIS Frontend

A317181 Consider primitive integer triangles as listed in rows of table A316842. Sequence gives 16*area^2 for these triangles in the same order.

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A331257 Numerator of squared radius of inscribed circle of the n-th triangle with integer sides in the list given by A316841. Denominators are A331258.

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Author

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PARI

Formula

A331258 Denominator of squared radius of inscribed circle of the n-th triangle with integer sides in the list given by A316841. Numerators are A331257.

Views

Author

Keywords

Examples

Crossrefs

Programs

PARI