A293137 a(0) = 0, and a(n) = floor(2*sqrt(n)) - 1 for n >= 1.
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, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 13, 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
Offset: 0
Keywords
Links
- Robert Israel, Table of n, a(n) for n = 0..10000
Programs
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Maple
0,seq(seq(k, n=ceil(((k+1)/2)^2) .. ceil(((k+2)/2)^2)-1),k=0..18); # Robert Israel, Oct 01 2017
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Mathematica
Join[{0}, Floor[2*Sqrt[Range[100]]] - 1] (* Paolo Xausa, Nov 13 2024 *) -
PARI
a(n)=if(n==0,0,floor(2*sqrt(n)) - 1);
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Python
from math import isqrt def A293137(n): return isqrt(n<<2)-1 if n else 0 # Chai Wah Wu, Jul 28 2022
Formula
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
Comments