Let T(n) denotes the number of non-congruent triangles with integer side lengths and perimeter n. Thus `T(1)=T(2)=T(3)=T(4)=0`, while `T(5)=1`. Prove that: (i) `T(2006)ltT(2009)` ii) `T(2005)=T(2008)`

Let T(n) denotes the number of non-congruent triangles with integer si

1.	Let T(n) denotes the number of non-congruent triangles with integer side lengths and perimeter n. Thus `T(1)=T(2)=T(3)=T(4)=0`, while `T(5)=1`. Prove that: (i) `T(2006)ltT(2009)` ii) `T(2005)=T(2008)`
Answer» a+b+c=n `T(n)=[(n+3)^2/48], n=odd` `T(n)=[n^2/48],n=even` 1)`T(2006)=[(2006)^2/48]` `T(2009)=[(2012)^2/48]` `T(2009)>T(2006)` 2)`T(2005)=[(2008)^2/48]=T(2005)`.

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Let T(n) denotes the number of non-congruent triangles with integer side lengths and perimeter n. Thus `T(1)=T(2)=T(3)=T(4)=0`, while `T(5)=1`. Prove that: (i) `T(2006)ltT(2009)` ii) `T(2005)=T(2008)`

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