recursive problem?

Question

Please solve following recursive equation step by step

f(n) = f(n-1)+2f(n-2)+3f(n-3) + n^2 (n>3)
f(0)=f(1)=f(2)=f(3)=1

Answer 1

f(n) = f(n - 1) + 2f(n - 2) + 3f(n - 3) + n^2 (n > 3)
f(0) = f(1) = f(2) = f(3) = 1
f(4) = f(3)+2f(2)+3f(1) + 4^2
f(4) = 1 + 2 +3 + 4^2 = 22
f(5) = 22 + 2 + 3 + 5^2 = 52
f(6) = 52 + 44 + 3 + 6^2 = 135
f(7) = 135 + 104 + 66 + 7^2 = 354
f(8) = 354 + 270 + 156 + 8^2 = 844
f(9) = 844 + 708 + 405 + 81 = 2,038
f(10) = 2,038 + 1688 + 1,062 + 100 = 4,888
f(11) = 4,888 + 4,076 + 2,532 + 121 = 11,617

-60564 + 63568.10476n - 28041.19722n^2 + 6756.995833n^3 - 963.9513889n^4 + 81.82083333n^5 - 3.851388889n^6 + 0.078571429n^7, 3 < n < 12

f(n) = n^2 + f(n - 1) + 2f(n - 2) + 3f(n - 3) (n > 3)
f(4) = 4^2 + 6
f(5) = 5^2 + f(4) + 2 + 3
f(5) = 5^2 + 4^2 + 11
f(6) = 6^2 + f(5) + 2f(4) + 3
f(6) = 6^2 + 5^2 + 3*4^2 + 26
f(7) = 7^2 + f(6) + 2f(5) + 3f(4)
f(7) = 7^2 + 6^2 + 3*5^2 + 8*4^2 + 66
f(8) = 8^2 + f(7) + 2f(6) + 3f(5)
f(8) = 8^2 + 7^2 + 3*6^2 + 8*5^2 + 17*4^2 + 151
f(9) = 9^2 + f(8) + 2f(7) + 3f(6)
edit:
Series within series.....
The integers look to be headed for a cubic relationship, as do the coeficients of the squared terms..might work more on this later if you leave it open....dunno if I can get anywhere with the squares, tho

Answer 2

a(n) = a(n-2) + a(n-a million) + n ; and a(2) = -2; a(a million) = a million Then a(6) is a(6) = a(5) + a(4) + 6 a(6) = [a(4) + a(3) + 5] + a(4) + 6 a(6) = 2* a(4) + a(3) + 11 a(6) = 2 * [ a(3) + a(2) + 4] + a(3) + 11 a(6) = 3* a(3) + 2*a(2) + 8 + 11 a(6) = 3*[ a(2) + a(a million) + 3] + 2 * a(2) + 19 a(6) = 3 * [ -2 + a million + 3] + 2 * (-2) + 19 a(6) = 21 alternately, operating backward: a(3) = a(2) + a(a million) + 3 = -2 + a million + 3 = 2 a(4) = a(3) + a(2) + 4 = 2 - 2 + 4 = 4 a(5) = a(4) + a(3) + 5 = 4 + 2 + 5 = 11 a(6) = a(5) + a(4) + 6 = 11 + 4 + 6 = 21 a(6) = 21 interior both circumstances.

Answer 3

I guess what raghuramk... c is getting at is that according to the equation,
f(3) = f(2) + 2f(1) + 3f(0) + 9
which is equal to 15,
whereas your data includes f(3) = 1.
so what's the correct information?:

Answer 4

There is something fishy. The definition you give for n>3 doesn't match with the defintion for f(3). I know it is possible logically but it doesn't smell good.

Answer 5

check your equations coorectly