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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.
3
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
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
KEYWORD
nonn,more
AUTHOR
Wolfdieter Lang, Aug 10 2020
STATUS
approved