poj2663 Tri Tiling

Tri Tiling Timelimit: 1000MSMemory Limit: 65536K Totalsubmissions: 5843Accepted: 3128

Description

In what many ways can you tile a 3xn rectangle with 2x1 dominoes?
Here is a sample tiling of a 3x12 rectangle.

Input

Input consists of several test cases followed by a line containing-1. Each test case was a line containing an integer 0 <= n <= 30.

Output

For each test case, the output one integer number giving the number of possible tilings.

Sample Input

2

8

12

-1

Sample Output

3

153

2131

Source

Waterloo Local 2005.09.24

__________________________________________________________

(Refer to Matrix67, image from Matrix67);

A total of 8 states, as above, the n+1 matrix multiplication, and then 000->111 as the answer.

__________________________________________________________

1 Program Stone;2 3 ConstA:Array[1..8,1..8] ofLongint= ((0,0,0,0,0,1,0,0),4 5(0,0,0,0,1,0,0,0),6 7(0,0,0,0,0,1,0,1),8 9(0,0,0,0,0,0,1,0),Ten  One(0,1,0,0,0,1,0,0), A  -(1,0,1,0,1,0,0,0), -  the(0,0,0,1,0,0,0,0), -  -(0,0,1,0,0,0,0,0)); -  + typeAr=Array[1..8,1..8] ofLongint; -  + varI,j,k,l,n:longint; A  at Qu,ti:ar; -  -   -  - Procedure Time (a,b:ar); -  in  varI,j,k:longint; -  to   begin +  -Fillchar (Ti,sizeof (TI),0); the  *      fori:=1  to 8  Do $ Panax Notoginseng       forj:=1  to 8  Do -  the        fork:=1  to 8  Do +  AInc (ti[i,j],a[i,k]*b[k,j]); the  +   End; -  $   $  - Procedure Quick (k:longint); -  the   begin - Wuyi    ifk=1  Then beginQu:=a;exit;End; the  -Quick (kDiv 2); Wu  - Time (qu,qu); About  $    ifKMoD 2<>0  ThenTime (ti,a); -  -qu:=ti; -  A   End; +  the   -  $ Begin the  theAssign (input,'input.in'); reset (input); the  the READLN (n); -  in    whilen<>-1  Do the  the    begin About  theQuick (n+1); the  theWriteln (qu[1,6]); +  - READLN (n); the Bayi    End; the  the close (input); -  - End.

poj2663 Tri Tiling