GNY07H  Tiling a Grid With Dominoes
We wish to tile a grid 4 units high and N units long with rectangles (dominoes) 2 units by one unit (in either orientation). For example, the figure shows the five different ways that a grid 4 units high and 2 units wide may be tiled.
Write a program that takes as input the width, W, of the grid and outputs the number of different ways to tile a 4byW grid.
Input
The first line of input contains a single integer N, (1 ≤ N ≤ 1000) which is the number of datasets that follow.
Each dataset contains a single decimal integer, the width, W, of the grid for this problem instance.
Output
For each problem instance, there is one line of output: The problem instance number as a decimal integer (start counting at one), a single space and the number of tilings of a 4byW grid. The values of W will be chosen so the count will fit in a 32bit integer.
Example
Input: 3 2 3 7 Output: 1 5 2 11 3 781
Added by:  Marco Gallotta 
Date:  20080312 
Time limit:  9.600s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel Pentium G860 3GHz) 
Languages:  All except: ERL JS NODEJS PERL 6 SCM chicken VB.net 
Resource:  ACM Greater New York Regionals 2007 
hide comments
Rishabh Joshi:
20150315 06:58:15
Very nice problem!! Learnt a lot! (hint: how can you start the series? Write all combinations of dominos by which you can start(and continue), and the answer will start to present itself)! 

Govind Lahoti:
20150213 08:45:32
Awesome problem. Enjoyed solving it :) 

mayank:
20141218 11:21:07
Tried after M3TILE. Almost similar. Could not get it straight though! :P 

fanatique:
20140701 19:25:33
good one :) 

Ravi Shankar Mondal:
20140624 21:34:24
100th green light :) 

Noob:
20140526 17:18:19
Good one! 

Himanshu:
20140130 06:33:30
Shouldn't input 3 give 5 + 2*5  1 = 14 as each tiling (except last) for input 2 can be widened by adding a column to the left or to the right. 

Ankit Kumar:
20131230 07:51:38
my 50th on SPOJ :) 

Hitman:
20131223 21:29:38
for n=0 ans=1 

nagato:
20130513 23:36:37
what is the range of W?? Last edit: 20130513 23:37:40 