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A188294
Array T(k,n)=[nr]-[kr]-[nr-kr], r=(1+sqrt(5))/2, read by antidiagonals.
13
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
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
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Mar 26 2011
STATUS
approved