I can't figure out this pattern: 1, 1, 4, 3, 9, 6, 16, 10, 25, 15, __, __, __, __

I think this may be right.

1,1,4,3,9,6,16,10,25,15,36,21,49,28,64,36,etc
1+2=3
3+3=6
6+4=10
10+5=15
15+6=21
21+7=28
28+8=36

Looks good to me. Alternating square numbers and triangular numbers.

To figure out the pattern in the given sequence: 1, 1, 4, 3, 9, 6, 16, 10, 25, 15, __, __, __, __, we need to look for any similarities or relationships between the numbers.

Let's analyze the sequence step by step:

First, we see that the sequence starts with the numbers 1 and 1.

Next, we have the number 4, which is the square of 2.

Then, we see the number 3, which is the sum of the previous two numbers.

After that, we have the number 9, which is the square of 3.

Following that, we have the number 6, which is the sum of the previous two numbers.

Next, we see the number 16, which is the square of 4.

Then, we have the number 10, which is the sum of the previous two numbers.

Continuing, we see the number 25, which is the square of 5.

Finally, we have the number 15, which is the sum of the previous two numbers.

To find the missing numbers in the sequence, we need to see the pattern we have identified so far.

First, we have a pair of squared numbers: 1, 4, 9, 16, 25.

Then, we have a pair of numbers that are the sum of the previous two numbers: 1+1=2, 3+2=5, 6+3=9, 10+6=16.

Based on this pattern, we can continue by squaring the next number, which is 6+10=16. The square of 16 is 256.

Similarly, we can add the next two numbers, 16 and 25, which gives us 41.

Therefore, the missing numbers in the sequence are 256, 41.

Hence, the complete sequence is 1, 1, 4, 3, 9, 6, 16, 10, 25, 15, 256, 41.