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 A347737 #24 Jun 07 2025 18:39:26
%S A347737 0,0,0,0,1,1,2,3,5,5,7,9,11,13,15,16,20,23,25,28,31,33,37,41,45,48,52,
%T A347737 54,59,64,67,72,78,81,86,89,94,100,106,110,116,122,126,132,138,141,
%U A347737 148,155,162,168,174,179,186,193,198,204,212,218,226,234,240,248,256,260
%N A347737 Zero together with the partial sums of A238005.
%C A347737 a(n) is also the total number of ones in the first n rows of A347579, n >= 1.
%F A347737 a(n) = A006463(n+1) - A060831(n).
%t A347737 Accumulate@Table[Length@Select[Select[IntegerPartitions@n,DuplicateFreeQ],Differences@MinMax@#=={Length@#}&],{n,60}] (* _Giorgos Kalogeropoulos_, Sep 12 2021 *)
%o A347737 (Python)
%o A347737 from math import isqrt
%o A347737 def A347737(n): return (r:=isqrt((n+1<<3)+1)-1>>1)*(6*n+4-r*(r+3))//6-((t:=isqrt(m:=n>>1))+(s:=isqrt(n)))*(t-s)-(sum(n//k for k in range(1,s+1))-sum(m//k for k in range(1,t+1))<<1) # _Chai Wah Wu_, Jun 07 2025
%Y A347737 a(n) is also the total number of zeros in the first n rows of the triangles A196020, A211343, A231345, A236106, A237048 (simpler), A239662, A261699, A271344, A272026, A280850, A285574, A285891, A285914, A286013, A296508 (and possibly others), n >= 1.
%Y A347737 Cf. A001227, A003056, A006463, A060831, A237593, A238005, A347579.
%K A347737 nonn
%O A347737 0,7
%A A347737 _Omar E. Pol_, Sep 11 2021