A240857 Triangle read by rows: T(0,0) = 0; T(n+1,k) = T(n,k+1), 0 <= k < n; T(n+1,n) = T(n,0); T(n+1,n+1) = T(n,0)+1.
0, 0, 1, 1, 0, 1, 0, 1, 1, 2, 1, 1, 2, 0, 1, 1, 2, 0, 1, 1, 2, 2, 0, 1, 1, 2, 1, 2, 0, 1, 1, 2, 1, 2, 2, 3, 1, 1, 2, 1, 2, 2, 3, 0, 1, 1, 2, 1, 2, 2, 3, 0, 1, 1, 2, 2, 1, 2, 2, 3, 0, 1, 1, 2, 1, 2, 1, 2, 2, 3, 0, 1, 1, 2, 1, 2, 2, 3, 2, 2, 3, 0, 1, 1, 2, 1
Offset: 0
Examples
. 0: 0 . 1: 0 1 . 2: 1 0 1 . 3: 0 1 1 2 . 4: 1 1 2 0 1 . 5: 1 2 0 1 1 2 . 6: 2 0 1 1 2 1 2 . 7: 0 1 1 2 1 2 2 3 . 8: 1 1 2 1 2 2 3 0 1 . 9: 1 2 1 2 2 3 0 1 1 2 . 10: 2 1 2 2 3 0 1 1 2 1 2 . 11: 1 2 2 3 0 1 1 2 1 2 2 3 . 12: 2 2 3 0 1 1 2 1 2 2 3 1 2 . 13: 2 3 0 1 1 2 1 2 2 3 1 2 2 3 . 14: 3 0 1 1 2 1 2 2 3 1 2 2 3 2 3 . 15: 0 1 1 2 1 2 2 3 1 2 2 3 2 3 3 4 .
Links
- Reinhard Zumkeller, Rows n = 0..125 of triangle, flattened
Crossrefs
Programs
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Haskell
a240857 n k = a240857_tabl !! n !! k a240857_row n = a240857_tabl !! n a240857_tabl = iterate (\(x:xs) -> xs ++ [x, x + 1]) [0]
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Mathematica
T[n_, k_] := DigitCount[n + k + 1, 2, 1] - 1; Table[T[n, k], {n, 0, 12}, {k, 0, n}] // Flatten (* Amiram Eldar, Aug 01 2023 *) -
Python
from math import isqrt def A240857(n): return (n-((r:=(m:=isqrt(k:=n+1<<1))+(k>m*(m+1)))*(r-3)>>1)).bit_count()-1 # Chai Wah Wu, Nov 11 2024
Comments