All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Numbers > Sequences
One harder sequence (Posted on 2011-05-24) Difficulty: 4 of 5
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

No Solution Yet Submitted by broll    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
re(2): One possible answer to what's next | Comment 5 of 6 |
(In reply to re: One possible answer to what's next by broll)

   0 _1_ ___2___ ___3___ ___4___ __5___ ...
1) 1 01 __02^3 __02^5 __02^7 _02^9 ...
2) 1 12 __02^3 __02^5 __02^7 _02^9 ...
3) 1 23 __12^3 __02^5 __02^7 _02^9 ...
4) 1 34 __52^3 __12^5 __02^7 _02^9 ...
5) 1 45 _152^3 __72^5 __12^7 _02^9 ...
6) 1 56 _352^3 _282^5 __92^7 _12^9 ...
7) 1 67 _702^3 _842^5 _452^7 112^9 ...
8) ...

0) 1
1) n(n+1)
2) binomial coefficients C(n, 4) 2^ 3
3) binomial coefficients C(n, 6) 2^ 5
4) binomial coefficients C(n, 8) 2^ 7
5) binomial coefficients C(n,10) 2^ 9
6) binomial coefficients C(n,12) 2^11
...
N) binomial coefficients C(n,2N) 2^(2N-1)

[The nth term for each sequence of binomial coefficient C(n, x) as it relates to the polynomial begins with 1 for the Nth coefficient of each  polynomial].

Edited on June 27, 2011, 1:16 pm
  Posted by Dej Mar on 2011-06-27 12:55:42

Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (8)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information