This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A367055 #32 Nov 12 2024 09:06:28 %S A367055 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, %T A367055 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, %U A367055 4,5,4,5,5,6,4,5,5,6,2,3,3,4,3,4,4,5,3 %N A367055 Triangle read by rows: T(n, k) = A000120(n) + A000120(k), 0 <= k <= n. %C A367055 T(n, k) is the sum of the Hamming weight of n and the Hamming weight of k. %C A367055 See A365618 for a table read by antidiagonals. %F A367055 T(n, k) = A000120(n) + A000120(k). %e A367055 Triangle begins: %e A367055 k=0 1 2 3 4 5 %e A367055 n=0: 0; %e A367055 n=1: 1, 2; %e A367055 n=2: 1, 2, 2; %e A367055 n=3: 2, 3, 3, 4; %e A367055 n=4: 1, 2, 2, 3, 2; %e A367055 n=5: 2, 3, 3, 4, 3, 4; %e A367055 ... %t A367055 T[n_, k_] := DigitCount[n, 2, 1] + DigitCount[k, 2, 1] %o A367055 (Python) %o A367055 from math import comb, isqrt %o A367055 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 %Y A367055 Cf. A000069, A000120, A000788, A001969, A365618. %K A367055 nonn,easy,tabl %O A367055 0,3 %A A367055 _Mithra Karamchedu_ and _Sophia Pi_, Nov 03 2023