A252055 Number of products A000201(i)*A001950(j) = n.

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, 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, 1, 3, 0, 1, 1, 1, 1, 1, 1, 3, 0, 4, 1, 0, 1, 3, 1, 2

Offset: 1

Author

Clark Kimberling, Dec 23 2014

Keywords

• nonn
• easy

Comments

A000201 and A001950 are the lower and upper Wythoff sequences, which partition the nonnegative integers.

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?

Examples

			a(312) counts these 7 products:  3*104, 4*78, 6*52, 8*39, 12*26, 24*13, 156*2
		

Links

• Clark Kimberling, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000201, A001950.

Programs

Maple

N:= 1000: # to get a(1) to a(N)
A201:= [seq(floor(n*phi),n=1..N)]:
A1950:= [seq(floor(n*phi^2),n=1..N)]:
A:= Vector(N):
for i from 1 to N do
  for j from 1 do
    m:= A201[i]*A1950[j];
    if m > N then break fi;
    A[m]:= A[m]+1;
   od
od:
convert(A,list); # Robert Israel, Dec 23 2014

Mathematica

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}]