# SICP 1.2.2 Tree recursion

*Published: 2020-06-14T19:06:09.000Z*

I like how they did not shown yet how to work with any data structures, but wrote function that behaves like a immutable array:

```
(define (first-denomination kinds-of-coins)
(cond ((= kinds-of-coins 1) 1)
((= kinds-of-coins 2) 5)
((= kinds-of-coins 3) 10)
((= kinds-of-coins 4) 25)
((= kinds-of-coins 5) 50)))
```

## Exercise 1.11

Functions should produce following sequence: 1, 2, 4, 11, 25, 59, 142 (Sequence A100550 in the On-Line Encyclopedia of Integer Sequences)

```
(define (next-f c d e)
(+ e (* 2 d) (* 3 c)))
(define (f n)
(if (< n 3)
n
(next-f (f (- n 3))
(f (- n 2))
(f (- n 1)))))
```

```
(define (f n)
(define (f-iter a b c n)
(if (< n 3)
c
(f-iter b c (next-f a b c) (- n 1))))
(f-iter 0 1 2 n))
```

Done.

## Exercise 1.12. Pascal triangle

```
(define (P row col)
(cond
((= col 1) 1) ; first number in row is 1
((= col row) 1) ; last number is 1 too
(else (+ ; otherwise it's sum of two number above
(P (- row 1) (- col 1))
(P (- row 1) col)))))
```

## Exercise 1.13

This is hard one for me, because I'm not so good with math. I'll skip this for now.