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A344334 a(n) is the number of large or small squares that are used to tile primitive squares of type 1 whose length of side is A344333(n).

%I A344334 #12 Jun 02 2021 22:43:29
%S A344334 20,90,272,468,650,1332,2900,3600,2450,7650,4160,6642,10388,16400,
%T A344334 10100,25578,14762,27540,20880,42048,50960,54900,28730,90650,60500,
%U A344334 38612,98100,50850,125712,142400,149940,65792,141570,116948,214650,83810,105300,265232,354368
%N A344334 a(n) is the number of large or small squares that are used to tile primitive squares of type 1 whose length of side is A344333(n).
%C A344334 Some notations: s = side of the tiled squares, a = side of small squares, b = side of large squares, and z = number of small squares = number of large squares.
%C A344334 Every term is of the form z = (a*b)^2 * (a^2+b^2) with gcd(a, b) = 1.
%C A344334 Every primitive square is composed of m = a*b * (a^2+b^2) elementary rectangles of length L = a^2+b^2 and width W = a*b, so with an area A = a*b * (a^2+b^2) = m.
%C A344334 This sequence is not increasing: a(9) = 2450 < a(8) = 3600.
%C A344334 Every term is even.
%C A344334 If a = 1 and b = n > 1, then number of squares z = n^2 * (n^2+1) is in A071253 \ {0,2}.
%D A344334 Ivan Yashchenko, Invitation to a Mathematical Festival, pp. 10 and 102, MSRI, Mathematical Circles Library, 2013.
%H A344334 <a href="/index/O#Olympiads">Index to sequences related to Olympiads</a>.
%e A344334 Square 10 x 10 with a = 1, b = 2, s = 10, z = 20.
%e A344334       ___ ___ _ ___ ___ _
%e A344334      |   |   |_|   |   |_|
%e A344334      |___|___|_|___|___|_|
%e A344334      |   |   |_|   |   |_| with 10 elementary 2 x 5 rectangles
%e A344334      |___|___|_|___|___|_|
%e A344334      |   |   |_|   |   |_|              ___ ___ _
%e A344334      |___|___|_|___|___|_|             |   |   |_|
%e A344334      |   |   |_|   |   |_|             |___|___|_|
%e A344334      |___|___|_|___|___|_|
%e A344334      |   |   |_|   |   |_|
%e A344334      |___|___|_|___|___|_|
%Y A344334 Cf. A344330, A344331, A344332, A344333.
%Y A344334 Cf. A071253 \ {0,2} is a subsequence.
%K A344334 nonn
%O A344334 1,1
%A A344334 _Bernard Schott_, Jun 02 2021