WC 1.3 Counting Tiles

Infinite number of tiles of length 1, 2 and 3 are given to you.
In how many ways can you make a single tile of length 'n' using the given tiles.
Given tiles can be added together to make bigger length tiles.

Note: One arrangement is different from another if length of tile used is different in atleast one position.

Output Specifications:

Give your answer as sum of answers for these 'n' :

10
100
1000000
1000000000
12345654321
9999999999999999

Note: Give your answer modulo 1000000007(10^9 + 7) as it can be a large number.
Read more about modulo operation(%) here

Examples:

for n = 3, ans = 4
Possible combinations : 1+1+1, 1+2, 2+1, 3

for n = 5, ans = 13

IMPORTANT MESSAGE: The correct solution for this question has been updated on 2nd July. Please try your previous solutions again. Any inconvenience caused is deeply regretted.


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