A367055 Triangle read by rows: T(n, k) = A000120(n) + A000120(k), 0 <= k <= n.

0, 1, 2, 1, 2, 2, 2, 3, 3, 4, 1, 2, 2, 3, 2, 2, 3, 3, 4, 3, 4, 2, 3, 3, 4, 3, 4, 4, 3, 4, 4, 5, 4, 5, 5, 6, 1, 2, 2, 3, 2, 3, 3, 4, 2, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3

Offset

0,3

Comments

T(n, k) is the sum of the Hamming weight of n and the Hamming weight of k.

See A365618 for a table read by antidiagonals.

Links

Table of n, a(n) for n=0..86.

Formula

T(n, k) = A000120(n) + A000120(k).

Example

Triangle begins:
      k=0  1  2  3  4  5
  n=0:  0;
  n=1:  1, 2;
  n=2:  1, 2, 2;
  n=3:  2, 3, 3, 4;
  n=4:  1, 2, 2, 3, 2;
  n=5:  2, 3, 3, 4, 3, 4;
        ...

Mathematica

T[n_, k_] := DigitCount[n, 2, 1] + DigitCount[k, 2, 1]

Prog

(Python)
from math import comb, isqrt
def A367055(n): return (n-comb(r:=(m:=isqrt(k:=n+1<<1))+(k>m*(m+1)), 2)).bit_count()+(r-1).bit_count() # Chai Wah Wu, Nov 11 2024

Crossrefs

Cf. A000069, A000120, A000788, A001969, A365618.

Sequence in context: A025800 A029258 A280128 * A354703 A070096 A319821

Adjacent sequences: A367052 A367053 A367054 * A367056 A367057 A367058

Keyword

nonn,easy,tabl

Author

Mithra Karamchedu and Sophia Pi, Nov 03 2023

Status

approved