cp's OEIS Frontend

A293137 a(0) = 0, and a(n) = floor(2*sqrt(n)) - 1 for n >= 1.

%I A293137 #47 Nov 13 2024 16:31:14
%S A293137 0,1,1,2,3,3,3,4,4,5,5,5,5,6,6,6,7,7,7,7,7,8,8,8,8,9,9,9,9,9,9,10,10,
%T A293137 10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,13,13,13,13,13,13,13,
%U A293137 13,14,14,14,14,14,14,14,15,15,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,17,17,17,17,17,17,17,17,17,17,18
%N A293137 a(0) = 0, and a(n) = floor(2*sqrt(n)) - 1 for n >= 1.
%C A293137 Conjecture: a(n) is index k of last nonzero entry in row n of A293136.
%H A293137 Robert Israel, <a href="/A293137/b293137.txt">Table of n, a(n) for n = 0..10000</a>
%F A293137 G.f.: (1-x)^(-1) * Sum_{k>=0} (x^(4*k^2+10*k+7)+x^((2*k+1)^2)+x^((2*k+2)^2)+x^(4*k^2+6*k+3)). - _Robert Israel_, Oct 01 2017
%p A293137 0,seq(seq(k, n=ceil(((k+1)/2)^2) .. ceil(((k+2)/2)^2)-1),k=0..18); # _Robert Israel_, Oct 01 2017
%t A293137 Join[{0}, Floor[2*Sqrt[Range[100]]] - 1] (* _Paolo Xausa_, Nov 13 2024 *)
%o A293137 (PARI) a(n)=if(n==0,0,floor(2*sqrt(n)) - 1);
%o A293137 (Python)
%o A293137 from math import isqrt
%o A293137 def A293137(n): return isqrt(n<<2)-1 if n else 0 # _Chai Wah Wu_, Jul 28 2022
%Y A293137 Cf. A293136, A059618.
%K A293137 nonn
%O A293137 0,4
%A A293137 _Joerg Arndt_, Oct 01 2017