Assn3Soln - 1. Find the generating functions for the...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 1. Find the generating functions for the following sequences: , 1 , 4 , 13 , . . . ( a n = 3 n- 1 2 ) 7 , 10 , 15 , 22 , . . . ( a n = n 2 + 2 n + 7 ) 3 , 3 , 3 , 3 , 4 , 5 , 6 , 7 , . . . ( a n = n for n 3 , a = a 1 = a 2 = 3 ) 2 , 1 , 5 , 7 , 17 , . . . ( a n = 2 n + 1 for n even, a n = 2 n- 1 for n odd) 1 1- 3 x is the GF for a n = 3 n , 1 1- 3 x- 1 1- x is the GF for a n = 3 n- 1, thus the result is 1 2 parenleftBig 1 1- 3 x- 1 1- x parenrightBig . The GF for a n = n 2 is x ( x +1) (1- x ) 3 , the GF for a n = n is x (1- x ) 2 , the result is x ( x +1) (1- x ) 3 + 2 x (1- x ) 2- 7 1- x . The GF is obtained from the GF for a n = n by adding the GF for 3 , 2 , 1 , , , , . . . , i.e., x (1- x ) 2 + 3 + 2 x + x 2 . a n = 2 n + (- 1) n , thus the GF is 1 1- 2 x + 1 1+ x . 2. Find the generating function for the number of partitions of n to distinct even summands....
View Full Document

Page1 / 3

Assn3Soln - 1. Find the generating functions for the...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online