A188294 Array T(k,n)=[nr]-[kr]-[nr-kr], r=(1+sqrt(5))/2, read by antidiagonals.

0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0

Offset

1

Comments

It is easy to prove that the array consists solely of 0's and 1's.

If k=n then T(k,n)=0; otherwise T(k,n)+T(n,k)=1.

See A188014 for connections to the infinite Fibonacci word.

Row 1: A096270

Row 2: A188009

Row 3: A188011

Row 4: A188014

Col 1: A188432

Col 2: A188433

Col 3: A188436

Col 4: A188467

Links

Table of n, a(n) for n=1..119.

Formula

T(k,n)=[nr]-[kr]-[nr-kr], r=(1+sqrt(5))/2, k>=1, n>=1.

Example

Northwest corner:
0 1 0 1 1 0 1 0 1 1 0 1 1 0 1 0 (A096270)
0 0 0 0 1 0 0 0 0 1 0 0 1 0 0 0 (A188009)
1 1 0 1 1 1 1 0 1 1 1 1 1 1 1 0 (A188011)
0 1 0 0 1 0 1 0 0 1 0 1 1 0 1 0 (A188014)
0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0

Mathematica

r=(1+5^(1/2))/2;
T[k_, n_]:=Floor[n*r]-Floor[k*r]-Floor[n*r-k*r]
TableForm[Table[T[n, k], {n, 1, 30}, {k, 1, 20}]]

Crossrefs

Cf. A188014, A096270, A126999.

Sequence in context: A342910 A341258 A285831 * A079101 A334941 A076478

Adjacent sequences: A188291 A188292 A188293 * A188295 A188296 A188297

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 26 2011

Status

approved