A194848 - OEIS

%I #13 Nov 05 2024 03:11:45

%S 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 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 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 Write n = C(i,3)+C(j,2)+C(k,1) with i>j>k>=0; sequence gives j values.

%C See A194847.

%D D. E. Knuth, The Art of Computer Programming, vol. 4A, Combinatorial Algorithms, Section 7.2.1.3, Eq. (20), p. 360.

%F Equals A056557(n) + 1.

%p See A194847.

%o (Python)

%o from math import isqrt, comb

%o from sympy import integer_nthroot

%o 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 The [i,j,k] values are [A194847, A194848, A056558].

%K nonn

%O 0,3

%A _N. J. A. Sloane_, Sep 03 2011