

A054876


Number of pairwise incongruent triangles with integer sides and positive integer area and second longest side of length n.


2



0, 0, 0, 1, 2, 0, 0, 1, 0, 3, 0, 2, 4, 1, 4, 1, 4, 0, 0, 6, 1, 0, 0, 3, 10, 5, 0, 4, 6, 6, 0, 1, 1, 7, 7, 2, 5, 1, 8, 10, 6, 2, 0, 2, 5, 0, 0, 3, 0, 13, 13, 14, 6, 0, 7, 5, 0, 8, 0, 14, 9, 1, 3, 1, 23, 3, 0, 13, 2, 9, 0, 6, 7, 9, 19, 4, 1, 12, 0, 14, 0, 8, 0
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OFFSET

1,5


LINKS

Amiram Eldar, Table of n, a(n) for n = 1..1000


EXAMPLE

a(10) is 3 because there are three different integersided, integerarea triangles with middle side length 10, namely [9,10,17], [10,10,12], and [10,10,16].


MATHEMATICA

okQ[x_, y_, z_] := If[x + y <=z, False, Module[{s = (x + y + z)/2}, IntegerQ[ Sqrt[s(sx)(sy)(sz)]]]]; a[n_] := Module[{num = 0}, Do[Do[If[okQ[x, n, z], num++], {x, 1, n}], {z, n, 2n}]; num]; Array[a, 100, 0] (* Amiram Eldar, Jun 19 2019 *)


CROSSREFS

Cf. A054875.
Sequence in context: A182034 A171912 A306605 * A109502 A323887 A323365
Adjacent sequences: A054873 A054874 A054875 * A054877 A054878 A054879


KEYWORD

nonn


AUTHOR

Henry Bottomley, May 26 2000


EXTENSIONS

Definition corrected and offset changed by James R. Buddenhagen, Jan 16 2012
More terms from Amiram Eldar, Jun 19 2019


STATUS

approved



