---------------------------------------
N= 3 C= 2

S case  2 (groups 1)
CSC
123

n= 3 c= 2 W(n,c)= 2
Count(S in front)= 1 Count(S in middle)=1-1=0 Count(S at end)=1-0=1

---------------------------------------
N= 4 C= 2

S case  2 (groups 2)
CSC
C SC
1234

S case  3 (groups 1)
CC S
1234
n= 4 c= 2 W(n,c)= 9
Count(S in front)= 4 Count(S in middle)=4-2=2 Count(S at end)=4-1=3

---------------------------------------
N= 5 C= 2

S case  2 (groups 3, 1)
CSC
C SC
C  SC
 CS C
12345

S case  3 (groups 2)
CC S
C C S
12345
n= 5 c= 2 W(n,c)= 24
Count(S in front)= 10 Count(S in middle)=10-4=6 Count(S at end)=10-2=8

---------------------------------------
N= 6 C= 2

S case  2 (groups 4, 2)
CSC
C SC
C  SC
C   SC
 CS C
 C S C
123456

S case  3 (groups 3, 1)
CC S
C C S
C  C S
 CC  S
123456
n= 6 c= 2 W(n,c)= 50
Count(S in front)= 20 Count(S in middle)=20-6=14 Count(S at end)=20-4=16

---------------------------------------
N= 7 C= 2

S case  2 (groups 5, 3, 1)
CSC
C SC
C  SC
C   SC
C    SC
 CS C
 C S C
 C  S C
  CS  C
1234567

S case  3 (groups 4, 2)
CC S
C C S
C  C S
C   C S
 CC  S
 C C  S
1234567
n= 7 c= 2 W(n,c)= 90
Count(S in front)= 35 Count(S in middle)=35-9=26 Count(S at end)=35-6=29

---------------------------------------
N= 8 C= 2

S case  2 (groups 6, 4, 2)
CSC
C SC
C  SC
C   SC
C    SC
C     SC
 CS C
 C S C
 C  S C
 C   S C
  CS  C
  C S  C
12345678

S case  3 (groups 5, 3, 1)
CC S
C C S
C  C S
C   C S
C    C S
 CC  S
 C C  S
 C  C  S
  CC   S
12345678
n= 8 c= 2 W(n,c)= 147
Count(S in front)= 56 Count(S in middle)=56-12=44 Count(S at end)=56-9=47

---------------------------------------
N= 9 C= 2

S case  2 (groups 7, 5, 3, 1)
CSC
C SC
C  SC
C   SC
C    SC
C     SC
C      SC
 CS C
 C S C
 C  S C
 C   S C
 C    S C
  CS  C
  C S  C
  C  S  C
   CS   C
123456789

S case  3 (groups 6, 4, 2)
CC S
C C S
C  C S
C   C S
C    C S
C     C S
 CC  S
 C C  S
 C  C  S
 C   C  S
  CC   S
  C C   S
123456789
n= 9 c= 2 W(n,c)= 224
Count(S in front)= 84 Count(S in middle)=84-16=68 Count(S at end)=84-12=72

---------------------------------------
N= 10 C= 2

S case  2 (groups 8, 6, 4, 2)
CSC
C SC
C  SC
C   SC
C    SC
C     SC
C      SC
C       SC
 CS C
 C S C
 C  S C
 C   S C
 C    S C
 C     S C
  CS  C
  C S  C
  C  S  C
  C   S  C
   CS   C
   C S   C
1234567890

S case  3 (groups 7, 5, 3, 1)
CC S
C C S
C  C S
C   C S
C    C S
C     C S
C      C S
 CC  S
 C C  S
 C  C  S
 C   C  S
 C    C  S
  CC   S
  C C   S
  C  C   S
   CC    S
1234567890
n= 10 c= 2 W(n,c)= 324
Count(S in front)= 120 Count(S in middle)=120-20=100 Count(S at end)=120-16=104