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Greetings from P (Posted on 2013-01-24) Difficulty: 2 of 5
Derive a formula for the number of partitions of n into parts that are odd and bigger than 1; e.g. a(12)=5 cases: 3+3+3+3, 5+7, 7+5, 3+9, 9+3.

Verify your formula by evaluating a(14).

No Solution Yet Submitted by Ady TZIDON    
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what if... | Comment 2 of 5 |

What if the order didn't matter in the sums: for example, 5+7 and 7+5 counted as only one way of adding to 12?

DECLARE SUB decompose (x#, b#)
DEFDBL A-Z
CLEAR , , 25000
DIM SHARED ct
CLS
FOR n = 1 TO 45
  ct = 0
  decompose n, 3
  PRINT n, ct
NEXT n

SUB decompose (x, b)
  IF x < b THEN EXIT SUB
  FOR addend = b TO x STEP 2
   IF addend = x THEN
    ct = ct + 1
   ELSE
    decompose x - addend, addend
   END IF
  NEXT
END SUB

1             0
2             0
3             1
4             0
5             1
6             1
7             1
8             1
9             2
10            2
11            2
12            3
13            3
14            4
15            5
16            5
17            6
18            8
19            8
20            10
21            12
22            13
23            15
24            18
25            20
26            23
27            27
28            30
29            34
30            40
31            44
32            50
33            58
34            64
35            73
36            83
37            92
38            104
39            118
40            131
41            147
42            166
43            184
44            206
45            232

  Posted by Charlie on 2013-01-24 15:04:11
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