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The number of triangles (up to congruence) with integer coordinates and perimeter in [n, n+1).
11

%I #25 Jan 02 2024 12:45:12

%S 1,2,2,6,7,11,15,26,24,42,41,66,60,83,99,126,127,176,179,219,217,302,

%T 283,374,366,456,446,551,573,640,667,808,805,938,936,1123,1078,1286,

%U 1276,1464,1487,1699,1710,1909,1912,2193,2161,2447,2489,2806,2749,3064,3111

%N The number of triangles (up to congruence) with integer coordinates and perimeter in [n, n+1).

%H Peter Kagey, <a href="/A298079/b298079.txt">Table of n, a(n) for n = 3..149</a>

%H Peter Kagey, <a href="https://codegolf.stackexchange.com/q/153106/53884">Integer Triangles with perimeter less than n</a>, Programming Puzzles & Code Golf Stack Exchange.

%H Peter Kagey, <a href="/A298079/a298079.hs.txt">Haskell program for A298079</a>.

%e For n = 3, all triangles with perimeter in [3, 4) are congruent to:

%e (0, 0), (0, 1), (1, 0) with perimeter 3.41....

%e For n = 4, all triangles with perimeter in [4, 5) are congruent to:

%e (0, 0), (0, 1), (1, 2) with perimeter 4.65..., or

%e (0, 0), (0, 2), (2, 0) with perimeter 4.82....

%e For n = 5, all triangles with perimeter in [5, 6) are congruent to:

%e (0, 0), (0, 2), (1, 2) with perimeter 5.23..., or

%e (0, 0), (1, 2), (2, 1) with perimeter 5.88....

%Y Cf. A051518, A298121.

%K nonn

%O 3,2

%A _Peter Kagey_, Jan 11 2018