Please find the general term of the sequence: 11,20,42,101,245,570,.... Thank for your help.?

The following is my work:

11,20,42,101,245,570,.....,T(n),...

 .9,..22,.59,144,.325,.... D1

....13,.37,.85,.181,.....D2

......24,.48,.96,......D3

D3 can be rewritten as 24, 24*2,24*2^2,...

This results suggest a pattern that

T(n)=an^2+bn+c+d[2^(n-1)]

=>

a+b+c+d=11

4a+2b+c+2d=20

9a+3b+c+4d=42

16a+4b+c+8d=101

Solving the system, get

a=-5.5

b=1.5

c=-9

d=24

Thus, T(n)=24[2^(n-1)]-5.5n^2+1.5n-9.

Check: 

11...20...42...101...245...570...1268...2723...5703...T(10),...

 .. 9...22....59....144....325...698....1455...2980...D1

......13...37....85.....181...373...757.....1525....D2

..........24...48....96.....192...384....768.....D3

The nth term of that sequence could be:

(1/5)n^5 - 2n^4 + 11n^3 - (55/2)n^2 + (383/10)n - 9