

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).


3



20, 90, 272, 468, 650, 1332, 2900, 3600, 2450, 7650, 4160, 6642, 10388, 16400, 10100, 25578, 14762, 27540, 20880, 42048, 50960, 54900, 28730, 90650, 60500, 38612, 98100, 50850, 125712, 142400, 149940, 65792, 141570, 116948, 214650, 83810, 105300, 265232, 354368
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

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.
Every term is of the form z = (a*b)^2 * (a^2+b^2) with gcd(a, b) = 1.
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.
This sequence is not increasing: a(9) = 2450 < a(8) = 3600.
Every term is even.
If a = 1 and b = n > 1, then number of squares z = n^2 * (n^2+1) is in A071253 \ {0,2}.


REFERENCES

Ivan Yashchenko, Invitation to a Mathematical Festival, pp. 10 and 102, MSRI, Mathematical Circles Library, 2013.


LINKS

Table of n, a(n) for n=1..39.
Index to sequences related to Olympiads.


EXAMPLE

Square 10 x 10 with a = 1, b = 2, s = 10, z = 20.
___ ___ _ ___ ___ _
  _  _
______________
  _  _ with 10 elementary 2 x 5 rectangles
______________
  _  _ ___ ___ _
______________   _
  _  _ _______
______________
  _  _
______________


CROSSREFS

Cf. A344330, A344331, A344332, A344333.
Cf. A071253 \ {0,2} is a subsequence.
Sequence in context: A264851 A345286 A338485 * A225882 A281768 A225892
Adjacent sequences: A344331 A344332 A344333 * A344335 A344336 A344337


KEYWORD

nonn


AUTHOR

Bernard Schott, Jun 02 2021


STATUS

approved



