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A328787 Number of distinct sizes of equilateral triangles with vertices in an equilateral triangular array of points with n rows.

%I A328787 #16 Oct 30 2019 02:23:46
%S A328787 1,2,4,6,8,11,14,17,21,25,28,33,38,43,49,54,59,66,73,80,87,93,100,109,
%T A328787 116,124,133,142,150,161,172,181,191,201,211,224,234,246,258,271,282,
%U A328787 295,307,319,333,346,359,375,389,403,420,435,448,465,482,499,514
%N A328787 Number of distinct sizes of equilateral triangles with vertices in an equilateral triangular array of points with n rows.
%C A328787 a(n) <= A024610(n-1) - 1.
%H A328787 Peter Kagey, <a href="/A328787/b328787.txt">Table of n, a(n) for n = 2..10000</a>
%e A328787 For n = 4, the a(4) = 4 sizes of equilateral triangles are 1, sqrt(3), 2, and 3. For example,
%e A328787      *         o         *              *
%e A328787     * *       * o       o o            o o
%e A328787    o o o     o o *     * o *          o o o
%e A328787   o o o o,  o * o o,  o o o o,  and  * o o *.
%e A328787 For n = 7, the a(7) = 11 equilateral triangles have side lengths 1, sqrt(3), 2, sqrt(7), 3, sqrt(12), sqrt(13), 4, sqrt(21), 5, and 6.
%Y A328787 Cf. A000332, A003136, A024610.
%Y A328787 A108279 is the analog for squares on square grids.
%K A328787 nonn
%O A328787 2,2
%A A328787 _Peter Kagey_, Oct 27 2019