Integer Sequeces: An On-Line Look-Up

Here's a fascinating site that I've only just begun to explore. It's an online encyclopedia for looking up integer sequences. Say you have a sequence like:
1, 4, 9, 16
and you want to know what the next number might be. Or, you want to know of a relationship between these numbers. Go to this site, type in the sequence and it'll return:
Well, I thought it would quickly tell me that this is a sequence of squares:
1*1=1
2*2=4
3*3=9
4*4=16
But, that didn't come right back. Instead I got the following:
Triangle giving a(n,r) = number of equivalence classes of Boolean
functions of n variables and range r=0..2^n under action of symmetric
group.

Triangular array T read by rows: T(n,k)=k^2 mod n, for
k=1,2,...,[n/2], n=2,3,...

Triangle T(n,k), 0<=k<=n, giving coefficients when output
sequence O_0, O_1, O_2, ... from transformation described in A059216
is expressed in terms of input sequence I_0, I_1, I_2, ...

Triangle read by rows giving numbers of paths in a lattice satisfying
certain conditions.

Array of coefficients of x in the expansions of
T(k,x)=(1+kx-(k-2)x^2)/(1-x)^4, k>-4.

Array read by antidiagonals, generated by the matrix M =
[1,1,1;1,N,1;1,1,1];.

Define predecessors of n, P(n), to consist of numbers whose binary
representation is obtained from that of n by replacing 10 by 01 or
changing a final 1 to a 0; then a(0)=1, a(n) = Sum f(P(n)), n>0.

The pattern is obvious.

s(1)t(n) + s(2)t(n-1) + ... + s(k)t(n-k+1), where k = [ n/2 ], s = (odd
natural numbers)


Squares arising in p=x^2+n, where p is the smallest prime of this form.
Smallest q squares > 0 so that q+n is a prime.

n^2 mod 18.

n^2 mod 19.

Finally, I saw something I was thinking of when I wrote the sequence, although I had not thought of the modular part.

Anyway, even though I got an unexpected answer, the site still looks pretty neat.

By the way, this is an example of what's wrong with someone being asked to "find the next number." If you don't know the rule, then there's nothing to say that whatever rule you want to use is not the correct rule. That is, without a criteria to select the rule, any rule can do. I believe this is the "Ugly Duck Theorem," but more on that later.