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A194882 Write n = C(i,4)+C(j,3)+C(k,2)+C(l,1) with i>j>k>l>=0; sequence gives i values.

%I A194882 #10 Dec 12 2024 09:26:47
%S A194882 3,4,4,4,4,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,
%T A194882 6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,
%U A194882 7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8
%N A194882 Write n = C(i,4)+C(j,3)+C(k,2)+C(l,1) with i>j>k>l>=0; sequence gives i values.
%C A194882 Each n >= 0 has a unique representation as n = C(i,4)+C(j,3)+C(k,2)+C(l.1) with i>j>k>l>=0. This is the combinatorial number system of degree t = 4, where we get [A194882, A194883, A194884, A127324]. For degree t = 3 see A194847.
%D A194882 D. E. Knuth, The Art of Computer Programming, vol. 4A, Combinatorial Algorithms, Section 7.2.1.3, Eq. (20), p. 360.
%F A194882 a(n) = m if n < binomial(m+1,4) and a(n) = m+1 otherwise where m = 1+floor((24*(n+2))^(1/4)). - _Chai Wah Wu_, Dec 10 2024
%o A194882 (Python)
%o A194882 from math import comb
%o A194882 from sympy import integer_nthroot
%o A194882 def A194882(n): return (m:=integer_nthroot(24*(n+2),4)[0]+1)+(n>=comb(m+1,4)) # _Chai Wah Wu_, Dec 10 2024
%Y A194882 Equals A127321 + 3.
%Y A194882 Cf. A194882-A194884, A127324, A194885; A194847, A194848, A056558, A194849.
%K A194882 nonn
%O A194882 0,1
%A A194882 _N. J. A. Sloane_, Sep 04 2011