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%I #26 Dec 24 2014 00:27:28
%S 0,1,0,0,1,1,1,1,0,1,0,1,1,0,2,1,0,2,0,2,1,1,1,1,0,1,0,3,0,2,1,1,0,2,
%T 0,1,0,1,2,2,1,2,0,2,2,0,1,1,1,1,0,2,0,3,1,1,1,1,0,6,0,1,1,1,1,1,0,1,
%U 1,3,0,1,1,1,1,1,1,3,0,4,1,0,1,3,1,2
%N Number of products A000201(i)*A001950(j) = n.
%C A000201 and A001950 are the lower and upper Wythoff sequences, which partition the nonnegative integers.
%C Does this sequence include every nonnegative integer? What is the maximal number of consecutive 0's? What is the maximal number of consecutive 1's?
%H Clark Kimberling, <a href="/A252055/b252055.txt">Table of n, a(n) for n = 1..1000</a>
%e a(312) counts these 7 products: 3*104, 4*78, 6*52, 8*39, 12*26, 24*13, 156*2
%p N:= 1000: # to get a(1) to a(N)
%p A201:= [seq(floor(n*phi),n=1..N)]:
%p A1950:= [seq(floor(n*phi^2),n=1..N)]:
%p A:= Vector(N):
%p for i from 1 to N do
%p for j from 1 do
%p m:= A201[i]*A1950[j];
%p if m > N then break fi;
%p A[m]:= A[m]+1;
%p od
%p od:
%p convert(A,list); # _Robert Israel_, Dec 23 2014
%t r = (1 + Sqrt[5])/2; s = r/(r - 1); t = Flatten[Table[Floor[r*j]*Floor[s*k], {j, 1, 300}, {k, 1, 300}]]; a[n_] := Count[t, n]; u = Table[a[n], {n, 1, 300}]
%Y Cf. A000201, A001950.
%K nonn,easy
%O 1,15
%A _Clark Kimberling_, Dec 23 2014
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