> #Attendence Q1: > #Is this in the OEIS, including 3, and what is A number? ; > #YES, A198633 ; > #Without 3, what is the OEIS A number? ; > #A79 ; > #Is the King tour mentioned in the OEIS in our meaning? ; > #YES. ; > ; > #Attendence Q2. ; > #How many members of Cn(n) are there with an Even number of 1s ; > #EvCn(1):=0 ; > #EvCn(2):=1 ; > #EvCn(3):=3 ; > #EvCn(4):=7 ; > #EvCn(5):=15 ; > #EvCn(6):=31 ; > #The answer is 2^(n-1)-1 ; > #and it's in the oeis, A225 ; > #How many are there with a number of 1's that is divisible by 4? ; > #for Cn(n), n from 1..n ; > #the sequence is 0,0,0,1,5,15,35,70,126, ; > #binomial(n,4) ; > #A332 ; > ; > #Attendence Q3: #List of the Neighbours of [1,1,1,1,1] in Bn(5) ; > S:= Bn(5)[1][32] Typesetting:-mprintslash([(S := {16, 24, 28, 30, 31})],[{16, 24, 28, 30, 31}]) ; > {seq(Bn(5)[2][i], i in S)} {[0, 1, 1, 1, 1], [1, 0, 1, 1, 1], [1, 1, 0, 1, 1], [1, 1, 1, 0, 1], [1, 1, 1, 1, 0]} ; > #How many neighbours does [1,1,1,1...,1] (1 repeats 10^100 times ) ; > #in Bn(10^100) have? ; > #nops(Bn(10^100)[1][2^1000]) ; > ; > #Attendence Q4: > #Is this sequence in OEIS? ; > #A318109 ; > ; > #Attendence Q5: > #Is this sequence in OEIS and what is the A number? ; > #A172 ; > #This is Franel number a(n) = Sum_{k = 0..n} binomial(n,k)^3. ; > #It mentions the diagonal sequence. ; > # ; > ;