Given that n is a whole number, what is the next expression in this series of expressions, each of which is valid for all n?
n^0,
2n+1,
8n^2+6n+1,
32n^3+40n^2+12n+1
(In reply to
One possible answer to what's next by Dej Mar)
Hi Dej!
You might like to try looking for patterns in the righthand diagonals i.e. the ones parallel to the series of 1's. To get you started, the next row is actually: 2048n^6+5632n^5+5760n^4+2688n^3+560n^2+42n+1
The last element in each row is 1; the penultimate one is A002378 in Sloane and the sum of the coefficients is A011900 in Sloane.
That should be enough of a hint for now, I think...
Edited on June 27, 2011, 9:04 am

Posted by broll
on 20110627 08:54:36 