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

 

Logo

Invitation: celebrating 50 years of OEIS, 250000 sequences, and Sloane's 75th, there will be a conference at DIMACS, Rutgers, Oct 9-10 2014.

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 September 1 10:14 EDT 2014. Contains 246291 sequences.