login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 23 12:19 EDT 2021. Contains 346259 sequences. (Running on oeis4.)