cp's OEIS Frontend

A052146 a(n) = floor((sqrt(1+8*n)-3)/2).

%I A052146 #17 Jun 27 2025 04:26:51
%S A052146 0,0,1,1,1,2,2,2,2,3,3,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,6,
%T A052146 6,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,10,10,
%U A052146 10,10,10,10,10,10,10,10,10,10,11,11,11,11,11,11,11
%N A052146 a(n) = floor((sqrt(1+8*n)-3)/2).
%D A052146 Richard P. Stanley, Enumerative Combinatorics, Vol. 2, Cambridge, 1999; see p. 450, Problem 7.2(d).
%H A052146 Amiram Eldar, <a href="/A052146/b052146.txt">Table of n, a(n) for n = 1..10000</a>
%F A052146 From _Amiram Eldar_, Jun 27 2025: (Start)
%F A052146 a(n) = A003056(n) - 1.
%F A052146 Sum_{n>=3} (-1)^(n+1)/a(n) = Pi/4 (A003881). (End)
%t A052146 Floor[(Sqrt[1 + 8 Range[100]] - 3)/2] (* _Wesley Ivan Hurt_, Oct 02 2021 *)
%o A052146 (PARI) a(n) = (sqrtint(1 + 8*n)-3)\2; \\ _Amiram Eldar_, Jun 27 2025
%Y A052146 Cf. A003056, A003881.
%K A052146 nonn,easy
%O A052146 1,6
%A A052146 _N. J. A. Sloane_, Jan 23 2000