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
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carofe82:
20180306 16:35:48
Find the recurrence relation. 

arvindkejriwal:
20170629 09:24:19
dp+bitmask 

prasoonbatham:
20170524 08:28:38
Nice problem :) Ac in one go.


sushantgokhale:
20170403 07:35:41
fantastic problem :) Last edit: 20170403 07:36:45 

vignesh97:
20160608 11:46:46
Good problem. AC in first attempt :p 

minhthai:
20160122 12:01:09
backtracking is ok :) 

birdie:
20160115 10:37:48
backtracking+dynamic programing 

Francky:
20151230 19:06:34
Image restored. 

quirk:
20151230 13:51:57
For those who need the image: http://imgur.com/nhxjwNe 

xxbloodysantaxx:
20150709 21:59:36
No Image found ! Link broken 
Added by:  Marco Gallotta 
Date:  20080312 
Time limit:  9.600s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: ERL JSRHINO NODEJS PERL6 VB.NET 
Resource:  ACM Greater New York Regionals 2007 