A367824 Array read by ascending antidiagonals: A(n, k) is the numerator of (R(n) - k)/(n + k), where R(n) is the digit reversal of n, with A(0, 0) = 1.
1, 1, -1, 1, 0, -1, 1, 1, -1, -1, 1, 1, 0, -1, -1, 1, 3, 1, -1, -3, -1, 1, 2, 1, 0, -1, -2, -1, 1, 5, 3, 1, -1, -3, -5, -1, 1, 3, 1, 1, 0, -1, -1, -3, -1, 1, 7, 5, 1, 1, -1, -1, -5, -7, -1, 1, 4, 3, 2, 1, 0, -1, -2, -3, -4, -1, 1, 0, 7, 5, 3, 1, -1, -3, -5, -7, -9, -1
Offset: 0
Examples
The array of the fractions begins: 1, -1, -1, -1, -1, -1, -1, -1, ... 1, 0, -1/3, -1/2, -3/5, -2/3, -5/7, -3/4, ... 1, 1/3, 0, -1/5, -1/3, -3/7, -1/2, -5/9, ... 1, 1/2, 1/5, 0, -1/7, -1/4, -1/3, -2/5, ... 1, 3/5, 1/3, 1/7, 0, -1/9, -1/5, -3/11, ... 1, 2/3, 3/7, 1/4, 1/9, 0, -1/11, -1/6, ... 1, 5/7, 1/2, 1/3, 1/5, 1/11, 0, -1/13, ... 1, 3/4, 5/9, 2/5, 3/11, 1/6, 1/13, 0, ... ... The array of the numerators begins: 1, -1, -1, -1, -1, -1, -1, -1, ... 1, 0, -1, -1, -3, -2, -5, -3, ... 1, 1, 0, -1, -1, -3, -1, -5, ... 1, 1, 1, 0, -1, -1, -1, -2, ... 1, 3, 1, 1, 0, -1, -1, -3, ... 1, 2, 3, 1, 1, 0, -1, -1, ... 1, 5, 1, 1, 1, 1, 0, -1, ... 1, 3, 5, 2, 3, 1, 1, 0, ... ...
Links
- Stefano Spezia, First 151 antidiagonals of the array
Crossrefs
Programs
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Mathematica
A[0,0]=1; A[n_,k_]:=Numerator[(FromDigits[Reverse[IntegerDigits[n]]]-k)/(n+k)]; Table[A[n-k,k],{n,0,11},{k,0,n}]//Flatten
Formula
A(1, n) = -A026741(n-1) for n > 0.
A(2, n) = -A060819(n-2) for n > 2.
A(3, n) = -A060789(n-3) for n > 3.
A(4, n) = -A106609(n-4) for n > 3.
A(5, n) = -A106611(n-5) for n > 4.
A(6, n) = -A051724(n-6) for n > 5.
A(7, n) = -A106615(n-7) for n > 6.
A(9, n) = -A106619(n-9) for n > 8.
A(10, n) = -A106612(n-10) for n > 9.
Comments