No 17

We all know and love the Triangular Numbers 1, 3, 6, 10, 15, 21 ...

and we all know and love the Square numbers 1, 4, 9, 16, 25 ...

but how often have we wondered if the only Square Triangular number is 1 ?

A little calculation might produce the next example.

A very much longer calculation may produce another.

However a change of lifestyle would be needed to find 41616, the fourth example.

And a lifetime may well be too short to find 1413721 the fifth example.

Consider the sequence 1, 6, 35, 204 ...

obtained from the recurrence relation u_n = 6u_n-1 - u_n-2 with u₁=1 and u₂= 6 .

Now square each term of this sequence.

Isn't that amazing!!??

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E-mail us at madrascollege.maths@fife.gov.uk

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