login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Today, Nov 11 2014, is the 4th anniversary of the launch of the new OEIS web site. 70,000 sequences have been added in these four years, all edited by volunteers. Please make a donation (tax deductible in the US) to help keep the OEIS running.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A102341 Areas of 'close-to-equilateral' integer triangles. 5
12, 120, 1848, 25080, 351780, 4890480, 68149872, 949077360, 13219419708, 184120982760, 2564481115560, 35718589344360, 497495864091732, 6929223155685600, 96511629630137568, 1344233586759971040, 18722758603319903340 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

A close-to-equilateral integer triangle is defined to be a triangle with integer sides and integer area such that the largest and smallest sides differ in length by unity. The first five close-to-equilateral integer triangles have sides (5, 5, 6), (17, 17, 16), (65, 65, 66), (241, 241, 240) and (901, 901, 902).

Next four terms are: {three sides a<b<c and area} { 46816, 46817, 46817, 949077360}, { 174725, 174725, 174726, 13219419708}, { 652080, 652081, 652081, 184120982760}, {2433601, 2433601, 2433602, 2564481115560}. Also, the first case {1,1,2,0} - integer triangle with zero area, fully appropriate to definition of 'close-to-equilateral' one, should be added. We have 12 cases and a weak conjecture is that the total number of the 'close-to-equilateral' triangles is finite. - Zak Seidov, Feb 23 2005

This is an infinite series; two sides are equal in length to the hypotenuse of almost 30-60 triangles and the third side alternates between that length +/- 1. - Dan Sanders (dan(AT)ified.ca), Oct 22 2005

LINKS

Table of n, a(n) for n=1..17.

Eric Weisstein's World of Mathematics, Heronian Triangle.

Steven Dutch, Almost 30-60 Triples

FORMULA

(2/3) [A007655(n+2) - (-1)^n*A001353(n+1) ] (conjectured). - Ralf Stephan, May 17 2007

Empirical g.f.: 12*x / ((x^2-14*x+1)*(x^2+4*x+1)). - Colin Barker, Apr 10 2013

EXAMPLE

a(2) = 120 because 120 is the area of a triangle with side lengths of 16, 17 and 17.

CROSSREFS

Sequence in context: A200163 A012565 A012621 * A174561 A009078 A221493

Adjacent sequences:  A102338 A102339 A102340 * A102342 A102343 A102344

KEYWORD

easy,nonn

AUTHOR

Johannes Koelman (Joc_Kay(AT)hotmail.com), Feb 20 2005

EXTENSIONS

More terms from Zak Seidov, Feb 23 2005

More terms from Dan Sanders (dan(AT)ified.ca), Oct 22 2005

STATUS

approved

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

Content is available under The OEIS End-User License Agreement .

Last modified November 23 05:04 EST 2014. Contains 249839 sequences.