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A189458 a(n) = n+[nr/s]+[nt/s]; r=2, s=sqrt(2), t=1+sqrt(2).

%I A189458 #13 Sep 08 2022 08:45:56
%S A189458 3,7,12,15,20,24,27,32,36,41,44,48,53,56,61,65,70,73,77,82,85,90,94,
%T A189458 97,102,106,111,114,119,123,126,131,135,140,143,147,152,155,160,164,
%U A189458 167,172,176,181,184,189,193,196,201,205,210,213,217,222,225,230,234,239,242,246,251,254,259,263,266,271,275,280,283,287,292,295,300,304,309,312,316,321,324,329,333,336,341
%N A189458 a(n) = n+[nr/s]+[nt/s]; r=2, s=sqrt(2), t=1+sqrt(2).
%C A189458 See A189457.
%H A189458 G. C. Greubel, <a href="/A189458/b189458.txt">Table of n, a(n) for n = 1..10000</a>
%t A189458 r=2; s=2^(1/2); t=1+2^(1/2);
%t A189458 a[n_] := n + Floor[n*s/r] + Floor[n*t/r];
%t A189458 b[n_] := n + Floor[n*r/s] + Floor[n*t/s];
%t A189458 c[n_] := n + Floor[n*r/t] + Floor[n*s/t];
%t A189458 Table[a[n], {n, 1, 120}]  (*A189457*)
%t A189458 Table[b[n], {n, 1, 120}]  (*A189458*)
%t A189458 Table[c[n], {n, 1, 120}]  (*A186222, conjectured*)
%t A189458 Table[n+Floor[(2n)/Sqrt[2]]+Floor[(n(1+Sqrt[2]))/Sqrt[2]],{n,90}] (* _Harvey P. Dale_, Feb 04 2015 *)
%o A189458 (PARI) vector(120, n, n+floor((2*n)/sqrt(2))+floor((n*(1+sqrt(2)))/sqrt(2))) \\ _G. C. Greubel_, Aug 19 2018
%o A189458 (Magma) [n+Floor((2*n)/Sqrt(2))+Floor((n*(1+Sqrt(2)))/Sqrt(2)): n in [1..120]]; // _G. C. Greubel_, Aug 19 2018
%Y A189458 Cf. A189457, A186222.
%K A189458 nonn
%O A189458 1,1
%A A189458 _Clark Kimberling_, Apr 22 2011