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1. La Fée Verte (absinthe@qoto.org)'s status on Tuesday, 08-Oct-2019 22:29:29 UTC La Fée Verte

   • 🎓 Dr. Freemo :jpf: 🇳🇱
   • Kyle

   @khird @freemo

   How's this look?
   def N(x):
   if (x < 0):
   return 0
   if (x == 0 or x == 1):
   return 1
   return N(x-1) + N(x-2)

   def N135(x):
   if (x < 0):
   return 0
   if (x == 0):
   return 1
   return (N135(x-1) + N135(x-3) + N135(x-5))

   def NArr(x, arr):
   if (x < 0):
   return 0
   if (x == 0):
   return 1
   return sum([NArr(x - i, arr) for i in arr])

   def main():
   for n in range(10):
   print(n, N(n))

   for n in range(10):
   print(n, N135(n))

   for n in range(10):
   print(n, NArr(n, [1,3,5]))

   if __name__ == "__main__":
   main()

   • 🎓 Dr. Freemo :jpf: 🇳🇱 repeated this.
   • La Fée Verte (absinthe@qoto.org)'s status on Tuesday, 08-Oct-2019 23:56:10 UTC La Fée Verte

     • 🎓 Dr. Freemo :jpf: 🇳🇱
     • Kyle

     @khird @freemo

     Okay, so with all that, here is the actual longhand using the permutations, but I am not sure how to handle this if I passed an array of numbers like in the 1,3,5 example

     def NFact(x):
     def fact(x):
     _fact = 1
     for i in range(1, x+1):
     _fact = _fact * i
     return _fact

     def r_NFact(num):
     twos = x - num
     ones = x - (2 * twos)
     if ones < 0:
     return 0
     return r_NFact(num - 1) + ( fact(num) // (fact(ones) * fact(twos)))
     return r_NFact(x)

     🎓 Dr. Freemo :jpf: 🇳🇱 repeated this.
   • 🎓 Dr. Freemo :jpf: 🇳🇱 (freemo@qoto.org)'s status on Wednesday, 09-Oct-2019 05:06:05 UTC 🎓 Dr. Freemo :jpf: 🇳🇱

     • Kyle

     @Absinthe

     Just a suggestion, if you use the binomial coefficient notation when talking about permutations you might find it much easier to reason over, at least I do.

     @khird

   • 🎓 Dr. Freemo :jpf: 🇳🇱 (freemo@qoto.org)'s status on Wednesday, 09-Oct-2019 10:41:53 UTC 🎓 Dr. Freemo :jpf: 🇳🇱

     • Kyle

     @Absinthe

     read as "k pick n"

     \[
     \binom{n}{k} = \frac{n!}{k! (n-k)!}
     \]

     @khird

   • 🎓 Dr. Freemo :jpf: 🇳🇱 (freemo@qoto.org)'s status on Wednesday, 09-Oct-2019 10:43:03 UTC 🎓 Dr. Freemo :jpf: 🇳🇱

     • Kyle

     @Absinthe

     read as "n choose k"

     \[
     \binom{n}{k} = \frac{n!}{k! (n-k)!}
     \]

     @khird