read `W:\Cl2.txt`
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Comp(n,S),NuC(n,S),SeqNuC(N,S),GFS(S,t),CompC(n,C),NuCompC(n,C),\

  SeqNuCompC(N,C)
PartitionsC1:=proc(n,m,C) local T,s,T1,t1:
option remember:
 if m<=0 then
  RETURN({}):
 elif n=m then
  RETURN({[m]}):
 elif n<m then
  RETURN({}):
 fi:
 T:={}:
 for s from 1 to m do
  if C(s)=true then
   T1:=PartitionsC1(n-m,s,C):
   T:=T union {seq([m,op(t1)],t1 in T1)}:
  fi:
 od:
 T:
end:
PartitionsC1(6,3,m->evalb(1=1))
               {[3, 3], [3, 2, 1], [3, 1, 1, 1]}
PartitionsC:=proc(n,C) local m,T,T1:
 T:={}:
 for m from 1 to n do
  if C(m)=true then
   T1:=PartitionsC1(n,m,C):
   T:=T union T1:
  fi:
 od:
end:

PartitionsC(7,m->evalb(1=1))
{[7], [4, 3], [5, 2], [6, 1], [3, 2, 2], [3, 3, 1], [4, 2, 1], 

  [5, 1, 1], [2, 2, 2, 1], [3, 2, 1, 1], [4, 1, 1, 1], 

  [2, 2, 1, 1, 1], [3, 1, 1, 1, 1], [2, 1, 1, 1, 1, 1], 

  [1, 1, 1, 1, 1, 1, 1]}
PartitionsC(7,m->evalb(m mod 2=1))
{[7], [3, 3, 1], [5, 1, 1], [3, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1]

  }
NuPartitionsC1:=proc(n,m,C) local T,s,T1:
option remember:
 if m<=0 then
  RETURN(0):
 elif n=m then
  RETURN(1):
 elif n<m then
  RETURN(0):
 fi:
 T:=0:
 for s from 1 to m do
  if C(s)=true then
   T1:=NuPartitionsC1(n-m,s,C):
   T:=T+T1:
  fi:
 od:
 T:
end:
NuPartitionsC:=proc(n,C) local m,T,T1:
 T:=0:
 if n=0 then
  RETURN(1):
 fi:
 for m from 1 to n do
  if C(m)=true then
   T1:=NuPartitionsC1(n,m,C):
   T:=T+T1:
  fi:
 od:
 T:
end:
NuPartitionsC(7,m->evalb(1=1))
                               15
NuPartitionsC(7,m->evalb(m mod 2=1))
                               5
SeqNuPartitionsC:=proc(N,C) local n:
 [seq(NuPartitionsC(n,C),n=0..N)]:
end:
SeqNuPartitionsC(30,m->evalb(m mod 5=1 or m mod 5=4)) # A003114
[1, 1, 1, 1, 2, 2, 3, 3, 4, 5, 6, 7, 9, 10, 12, 14, 17, 19, 23, 

  26, 31, 35, 41, 46, 54, 61, 70, 79, 91, 102, 117]
SeqNuPartitionsC(30,m->evalb(m mod 5=2 or m mod 5=3)) # A003106
[1, 0, 1, 1, 1, 1, 2, 2, 3, 3, 4, 4, 6, 6, 8, 9, 11, 12, 15, 16, 

  20, 22, 26, 29, 35, 38, 45, 50, 58, 64, 75]
SeqNuPartitionsC(30,m->evalb(m mod 7=1 or m mod 7=2 or m mod 7=4)) # Not on OEIS
[1, 1, 2, 2, 4, 4, 6, 6, 10, 11, 15, 17, 23, 26, 32, 37, 47, 54, 

  66, 76, 93, 105, 126, 143, 172, 194, 230, 261, 306, 345, 401]