A336886 a(n) gives the number of all non-right angle triangles with pair of legs (X(n)_j, Y(n)_j) and base Z(n), where X(n)_j = sqrt(x(n)_j), Y(n)_j = sqrt(y(n)_j) and Z(n) = sqrt(z(n)), with integers x(n)_j <= y(n)_j <= z(n), such that the areas A(n)_j are positive integers, for j = 1, 2, ..., a(n). This implies that z(n) = A334818(n), for n >= 1.

1, 1, 1, 3, 2, 1, 4, 4, 2, 10, 1, 7, 7, 1, 8, 3, 9, 9, 1, 11, 10, 2, 20

Offset

1,4

Links

Table of n, a(n) for n=1..23.

Formula

The length of row n of the irregular triangle A336885 is 2*a(n), for n >= 1.

Example

a(4) = 3 because the three pairs (x(4)_j, y(4)_j), for j = 1, 2 , 3 = a(4), with z(4) =  A334818(4) = 10, are (2, 4), (4, 10) and (8, 10), with areas  A336887(4, 1) = 1,  A336887(4, 2) = 3 and  A336887(4, 3) = 4, respectively.

Crossrefs

Cf. A334818, A336885, A336887 (areas).

Sequence in context: A127671 A271724 A247641 * A261876 A272336 A210797

Adjacent sequences: A336883 A336884 A336885 * A336887 A336888 A336889

Keyword

nonn,more

Author

Wolfdieter Lang, Aug 10 2020

Status

approved