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
hide comments
sleepntsheep:
20230416 05:03:20
Can be solved with plug dp 

sanskar_native:
20210528 20:16:32
Can be solved using dp with bitmask...see William Fiset's YouTube channels for "Tilling Problem" explanation :) 

distructo:
20201228 09:59:59
https://www.spoj.com/problems/M3TILE/


sharjeel_spoj:
20201001 21:10:50
Why is it tagged #bitmasks? Can somebody point how to solve with bitmasks?


zakir068:
20200330 08:27:09
for w=0 ans = 1


lnxdx:
20191004 15:23:36
Two ACs in two goes :/ 

lnxdx:
20181123 17:31:55
The values of W will be chosen so the count will fit in a 32bit integer.


ushould_study:
20180913 15:07:12
how to define the size of w ? Is there any upper limit to it?


ayusofayush:
20180817 15:51:36
http://journeywithdp.blogspot.com/2018/07/waytosolvetilingproblems.html


karan_yadav:
20180805 13:42:00
Before solving this problem solve (https://www.spoj.com/problems/M3TILE/) Last edit: 20180805 13:42:13 
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 