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 A194848 #13 Nov 05 2024 03:11:45 %S A194848 1,1,2,2,1,2,2,3,3,3,1,2,2,3,3,3,4,4,4,4,1,2,2,3,3,3,4,4,4,4,5,5,5,5, %T A194848 5,1,2,2,3,3,3,4,4,4,4,5,5,5,5,5,6,6,6,6,6,6,1,2,2,3,3,3,4,4,4,4,5,5, %U A194848 5,5,5,6,6,6,6,6,6,7,7,7,7,7,7,7,1,2,2,3,3,3,4,4,4,4,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,1,2,2 %N A194848 Write n = C(i,3)+C(j,2)+C(k,1) with i>j>k>=0; sequence gives j values. %C A194848 See A194847. %D A194848 D. E. Knuth, The Art of Computer Programming, vol. 4A, Combinatorial Algorithms, Section 7.2.1.3, Eq. (20), p. 360. %F A194848 Equals A056557(n) + 1. %p A194848 See A194847. %o A194848 (Python) %o A194848 from math import isqrt, comb %o A194848 from sympy import integer_nthroot %o A194848 def A194848(n): return (k:=isqrt(r:=n+1-comb((m:=integer_nthroot(6*(n+1),3)[0])-(n<comb(m+2,3))+2,3)<<1))+((r<<2)>(k<<2)*(k+1)+1) # _Chai Wah Wu_, Nov 04 2024 %Y A194848 The [i,j,k] values are [A194847, A194848, A056558]. %K A194848 nonn %O A194848 0,3 %A A194848 _N. J. A. Sloane_, Sep 03 2011