What are 3 different ways to complete this pattern : 1,1,2,3 _ , _, _ ?

Question

Also it would be helpful if you could explain them.

Answer 1

1,1,2,3,5,8,13
Fibonacci series--The next number is the sum of the two pervious numbers.

1,1,2,3,3,4,5,5,6,7,7,8,9,9..
odd numbers appear twice, even numbers once, and then number increases by 1

1,1,2,3,4,4,5,6,6,7,8,8,9,9,10,10,11,12,12..
prime numbers appear twice, non-prime numbers once, and then number increases by 1

1,1,2,3,4,4,5,6,7,8,9,9,10,11,12,
perfect squares appear twice, non-perfect squares appear once

1,1,2,3,4,4,4,5,6,7,8,9,9,9,9,9,9,9,9,9,9,10,11,12
let the perfect square =x^2
the perfect squares appear x^2+1 times, non-perfect square appear once


1,1,2,3,4,4,4,5,6,7,8,9,9,9,9,10,11,12
let the perfect square =x^2
the perfect squares appear x+1 times, non-perfect square appear once

Answer 2

1, 1, 2, 3, 5, 8, 13 (x_n = x_(n-1) + x_(n-2); x_0=1, x_1=1 - this is also known as the fibonacci sequence)

1, 1, 2, 3, 3, 1, -4 (x_n = -1/6 n³ + n² - 5/6 n + 1 - this is the unique third-degree polynomial that passes through all of the first four points)

1, 1, 2, 3, 8, 15, 48 (x_n = n!/x_(n-1); x_0=1 - this one I just made up).

Answer 3

I'm only seeing the Fibonacci sequence
5, 8, 13

If you didn't have the two 1's in the beginning then you could go w/ prime numbers for
5, 7, 11

Answer 4

I got three:
1,1,2,3,5,8,13 - Fibonacci
1,1,2,3,1,4,5 - the integers with an extra 1 every 4th digit
1,1,2,3,3,2,1,1 - symmetrical

Answer 5

3, 4, 5
4,4,5
4,5,5

Answer 6

1,1,2,3,5,8,13

get the sum of the last two numbers ;)

Answer 7

1,1,2,3 2,2,3,4

1,1,2,3 4,4,5,6

1,1,2,3 4,5,6,7

Answer 8

3,4,4
4,4,5
4,5,5