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A252055 Number of products A000201(i)*A001950(j) = n. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,15

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?

LINKS

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

EXAMPLE

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

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}]

CROSSREFS

Cf. A000201, A001950.

Sequence in context: A140397 A120614 A287516 * A324144 A320836 A097567

Adjacent sequences:  A252052 A252053 A252054 * A252056 A252057 A252058

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Dec 23 2014

STATUS

approved

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Last modified April 18 19:31 EDT 2021. Contains 343089 sequences. (Running on oeis4.)