cp's OEIS Frontend

A360010 First part of the n-th weakly decreasing triple of positive integers sorted lexicographically. Each n > 0 is repeated A000217(n) times.

%I A360010 #12 Nov 05 2024 12:19:11
%S A360010 1,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,
%T A360010 5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,
%U A360010 7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8
%N A360010 First part of the n-th weakly decreasing triple of positive integers sorted lexicographically. Each n > 0 is repeated A000217(n) times.
%F A360010 a(n) = A056556(n) + 1 = A331195(3n) + 1.
%F A360010 Sum_{n>=1} (-1)^(n+1)/a(n) = Pi/8 + log(2)/4. - _Amiram Eldar_, Feb 18 2024
%F A360010 a(n) = m+1 if n>binomial(m+2,3) and a(n) = m otherwise where m = floor((6n)^(1/3)). - _Chai Wah Wu_, Nov 04 2024
%e A360010 Triples begin: (1,1,1), (2,1,1), (2,2,1), (2,2,2), (3,1,1), (3,2,1), (3,2,2), (3,3,1), (3,3,2), (3,3,3), ...
%t A360010 nn=9;First/@Select[Tuples[Range[nn],3],GreaterEqual@@#&]
%o A360010 (Python)
%o A360010 from math import comb
%o A360010 from sympy import integer_nthroot
%o A360010 def A360010(n): return (m:=integer_nthroot(6*n,3)[0])+(n>comb(m+2,3)) # _Chai Wah Wu_, Nov 04 2024
%Y A360010 For pairs instead of triples we have A002024.
%Y A360010 Positions of first appearances are A050407(n+2) = A000292(n)+1.
%Y A360010 The zero-based version is A056556.
%Y A360010 The triples have sums A070770.
%Y A360010 The second instead of first part is A194848.
%Y A360010 The third instead of first part is A333516.
%Y A360010 Concatenating all the triples gives A360240.
%Y A360010 Cf. A000217, A003056, A056557, A056558, A069905, A158842, A331195.
%K A360010 nonn
%O A360010 1,2
%A A360010 _Gus Wiseman_, Feb 11 2023