> #There are  4  Attendance Problems 
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> 
;
> #Q1
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> #Let K be the 3-digit number consisting of your 3rd, 4th, 5th RUID digits, what is g(K)
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> 
;
> #K = 900
;
> #g(K) = g(899)+g(897)+g(896) = g(898)+g(896)+g(895)+g(986)+g(894)+g(893)+g(985)+g(893)+g(892) =...
;
> 
;
> #Q2
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> #Is {g(n)} in the OEIS? IF YES WHAT IS THE A-number IF NOT
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> #Should be?
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> 
> #we know g(n) = 1, 1, 0, 1 (n = 0, 1, 2, 3)
;
> #g(4) = g(3)+g(1)+g(0) = 3
;
> #g(5) = g(4)+g(2)+g(1) = 4
;
> #g(6) = g(5)+g(3)+g(2) = 5
;
> #g(7) = g(6)+g(4)+g(3) = 9
;
> #g(8) = g(7)+g(5)+g(4) = 16...
;
> #Search 1,1,0,1,3,4,5,9,16 found no result on OEIS
;
> #It should be.
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> 
;
> #Q3
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> #For i=3,4,5...
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> #Compute SeqRec([[1$i],[0$(i-1),1]],30);
> #Find whether these sequences are in the oeis
;
> #Find their A-numbers
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> #What is the smallest i for which this sequence is not in the oeis?
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> #Should it be?
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> 
;
> Rec:=proc(P,n)  local L, INI,k,i:
> option remember:
> 
> #We first unpack P
> L:=P[1]:
> INI:=P[2]:
> 
> k:=nops(L):
> 
> if nops(INI)<>k then
>  print(INI, `should have`, k, `entries `):
>  RETURN(FAIL):
> fi:
> 
> 
> if n<k then
> #For this case we use the initial condition, since list in Maple start at index 1, we need to access INI[n+1]
>  RETURN(INI[n+1]):
> else
> #We use the definig recurrence
> add(L[i]*Rec(P,n-i),i=1..k):
> fi:
> 
> end:

> SeqRec:=proc(P,N) local n:
> [seq(Rec(P,n),n=0..N)]:
> end:
> SeqRec([[1$3],[0$(3-1),1]],30)
[0, 0, 1, 1, 2, 4, 7, 13, 24, 44, 81, 149, 274, 504, 927, 1705, 3136, 5768, 10609, 19513, 35890, 66012, 121415, 223317, 410744, 755476, 1389537, 2555757, 4700770, 8646064, 15902591]
;
> #IN THE OEIS, A-NUMBER IS A000073
;
> 
;
> SeqRec([[1$4],[0$(4-1),1]],30)
[0, 0, 0, 1, 1, 2, 4, 8, 15, 29, 56, 108, 208, 401, 773, 1490, 2872, 5536, 10671, 20569, 39648, 76424, 147312, 283953, 547337, 1055026, 2033628, 3919944, 7555935, 14564533, 28074040]
;
> #IN THE OEIS, A-NUMBER IS A000078
;
> SeqRec([[1$5],[0$(5-1),1]],30)
[0, 0, 0, 0, 1, 1, 2, 4, 8, 16, 31, 61, 120, 236, 464, 912, 1793, 3525, 6930, 13624, 26784, 52656, 103519, 203513, 400096, 786568, 1546352, 3040048, 5976577, 11749641, 23099186]
;
> #IN THE OEIS, A-NUMBER IS A001591
;
> SeqRec([[1$14],[0$(14-1),1]],30)
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16383, 32765, 65528]
;
> #the smallest i for this sequence is not in the oeis is 14, it should be
;
> 
;
> #Q4
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> #Let a := 2nd digit of your ruid (0->1) b := 7th digit
;
> #What is the 100th term of #GFseq(1/1-x^a-x^b)
;
> 
;
> GFseq:=proc(f,x,N) local  f1,i:
> f1:=taylor(f,x=0,N+1):
> [seq(coeff(f1,x,i),i=0..N)]:
> end:

> GFseq(x/(1-x^7-x^5),x,100);
[0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 2, 0, 1, 1, 0, 3, 0, 3, 1, 1, 4, 0, 6, 1, 4, 5, 1, 10, 1, 10, 6, 5, 15, 2, 20, 7, 15, 21, 7, 35, 9, 35, 28, 22, 56, 16, 70, 37, 57, 84, 38, 126, 53, 127, 121, 95, 210, 91, 253, 174, 222, 331, 186, 463, 265, 475, 505, 408, 794, 451, 938, 770, 883, 1299, 859, 1732, 1221, 1821, 2069, 1742, 3031, 2080, 3553, 3290, 3563, 5100, 3822, 6584, 5370, 7116, 8390, 7385, 11684, 9192, 13700, 13760, 14501, 20074]
;
> #So the 100th term is 14501
;