let t(n) denote the number of integer sided triangle with distinct sides chosen from(1,2,3...n) then t(20)-t(19) equals

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- Oct 2nd 2010, 12:01 AMprasumtriangle problem
let t(n) denote the number of integer sided triangle with distinct sides chosen from(1,2,3...n) then t(20)-t(19) equals

- Oct 2nd 2010, 03:14 AMWilmer
Go here: The On-Line Encyclopedia of Integer Sequences™ (OEIS™)

Enter sequence number A002623 - Oct 2nd 2010, 04:22 AMprasum
but how will i know this sequence

- Oct 2nd 2010, 04:56 AMprasum
but they are integral sided triangles

- Oct 2nd 2010, 07:53 AMWilmer
I'm no longer sure I know what you're asking...or that you know what you're asking!

OK, answer this: using n=3, thus (1,2,3), how many integer sided triangles can you construct?

And list them, please: there's not many. - Oct 2nd 2010, 08:13 AMundefined
I believe your question is very similar to this one

http://www.mathhelpforum.com/math-he...es-148807.html

Ignore my initial comments where I misinterpreted what was being asked. - Oct 2nd 2010, 08:31 AMTraveller
The answer to the OP's question is the number of triangles with integer sides and at least one side 20. The sum of the other two sides can vary from 21 to 40. So we can have 10 + 2* (11 + 12 + ... + 19 ) + 20 = 10 + 2*135 + 20 = 300.

EDIT : Sorry, overlooked the distinct sides part. The number of such isosceles triangles is 9 + 20 = 29. So the answer should be 300 - 29 = 271. - Oct 2nd 2010, 08:47 AMundefined
Hmm I think your number is too high because for example wouldn't you get the 19 in parentheses by considering these triangles?

{20,1,38}

{20,2,36}

...

{20,19,19}

and

{20,1,39}

{20,2,37}

...

{20,19,20}

But a side length cannot be greater than 20.

I get 81 as explained in post #25 here, which I probably should have referenced before. - Oct 2nd 2010, 09:05 AMTraveller
My bad, thank you for the rectification. It is 81.

- Oct 2nd 2010, 09:40 AMWilmer