A227984 Triangle T(n,k), read by rows: T(n,k) is the numerator of (1-2^(n-k+1))/(1-2^(k+1)).
1, 3, 1, 7, 1, 1, 15, 7, 3, 1, 31, 5, 1, 1, 1, 63, 31, 15, 7, 3, 1, 127, 21, 31, 1, 7, 1, 1, 255, 127, 9, 31, 15, 1, 3, 1, 511, 85, 127, 21, 1, 5, 7, 1, 1, 1023, 511, 255, 127, 63, 31, 15, 7, 3, 1, 2047, 341, 73, 17, 127, 1, 31, 1, 1, 1, 1, 4095, 2047, 1023
Offset: 0
Examples
Triangle begins: 1; 3, 1; 7, 1, 1; 15, 7, 3, 1; 31, 5, 1, 1, 1; 63, 31, 15, 7, 3, 1; 127, 21, 31, 1, 7, 1, 1; 255, 127, 9, 31, 15, 1, 3, 1; 511, 85, 127, 21, 1, 5, 7, 1, 1; 1023, 511, 255, 127, 63, 31, 15, 7, 3, 1; 2047, 341, 73, 17, 127, 1, 31, 1, 1, 1, 1; etc.
Links
- Vincenzo Librandi, Rows n = 0..100, flattened
Programs
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Magma
[Numerator((1-2^(n-k+1))/(1-2^(k+1))): k in [0..n], n in [0..11]];
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Mathematica
a[n_, k_] := Numerator[(1 - 2^(n - k + 1))/(1 - 2^(k + 1))]; Table[a[n, k], {n, 0, 11}, {k, 0, n}] // Flatten
Comments