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# Step I, 2007, Q1 watch

1. (Original post by generalebriety)
Ah, ok. Might feed it into Maple and see if it factorises at all.
A slightly nicer polynomial is:

Edit: k(k+1) are factors, and I find one other root numerically.
2. (Original post by ukgea)
Without resorting to cheating (*ahem* :P), I get it to be

Spoiler:
Show

Thinking about it, it should be

Spoiler:
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That gives the values

k=1: 10
k=2: 96
k=3: 445
k=4: 1431
k=5: 3681
k=6: 8141
k=7: 16142
k=8: 29466
k=9: 50412

for k = 1 through 5, the values are the same as the values given by DFranklin's formula, but for k >= 6 DFranklin's formula starts growing faster. Which is very weird, because both formulae are polynomials of degree 5, I think, so they should be equal. Did I make a mistake in my calculations somewhere? ???
3. I think your numbers are correct (well done - I have no idea where your expression comes from, but it obviously works).

I don't know if I've managed to make a transcription error somewhere - this is the exact code I have for the polynomial (cut/pasted from Visual Studio):

k*(10+(k-1)*(38+(k-2)*(187/6.0+(k-3)*(187/24.0+11*(k-4)/20.0))));

and this gives the same numbers for k=1 to 9 as those you provide (evaluated by computer, obviously).

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Updated: July 14, 2007
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