A184625 -id:A184625 - cp's OEIS frontend

A184676 a(n) = n + floor((n/2-1/(4*n))^2); complement of A183867.

1, 2, 5, 7, 11, 14, 19, 23, 29, 34, 41, 47, 55, 62, 71, 79, 89, 98, 109, 119, 131, 142, 155, 167, 181, 194, 209, 223, 239, 254, 271, 287, 305, 322, 341, 359, 379, 398, 419, 439, 461, 482, 505, 527, 551, 574, 599, 623, 649, 674, 701, 727, 755, 782, 811, 839

Offset: 1

Clark Kimberling, Jan 19 2011

a(n) is also the number of trees with n vertices with diameter (n-3). - Erich Friedman, Apr 06 2017

Nathaniel Johnston, Table of n, a(n) for n = 1..5000
Index entries for linear recurrences with constant coefficients, signature (2,0,-2,1).

Cf. A183867, A184625, A198442.

[n+Floor((n/2-1/(4*n))^2): n in [1..60]]; // Vincenzo Librandi, Dec 09 2015

seq(n+floor((n/2-1/(4*n))^2), n=1..56); # Nathaniel Johnston, Jun 26 2011

a[n_]:=n+Floor[(n/2-1/(4n))^2];
b[n_]:=n+Floor[n^(1/2)+(n+1/2)^(1/2)];
Table[a[n],{n,1,120}]   (* A184676 *)
Table[b[n],{n,1,120}]   (* A183867 *)
FindLinearRecurrence[Table[a[n],{n,1,120}]]
LinearRecurrence[{2,0,-2,1},{1,2,5,7},56] (* Ray Chandler, Aug 02 2015 *)
Table[n + Floor[(n/2 - 1/(4 n))^2], {n, 60}] (* Vincenzo Librandi, Dec 09 2015 *)
Table[Ceiling[n/2] (2 + Ceiling[n/2] - Mod[n, 2]) - 1, {n, 1, 56}] (* Fred Daniel Kline, Jun 24 2016 *)

a(n) = n+floor((n/2-1/(4*n))^2); \\ Michel Marcus, Dec 09 2015

a(n) = n+floor((n/2-1/(4*n))^2).
a(n) = A198442(n+2)-1. - Fred Daniel Kline, Jun 24 2016
G.f.: x*(1 + x^2 - x^3)/((1 - x)^3*(1 + x)). - Ilya Gutkovskiy, Jun 24 2016

A184624 a(n) = floor(n*r +h), where r=sqrt(2), h=-1/4; complement of A184619.

Original entry on oeis.org

1, 2, 3, 5, 6, 8, 9, 11, 12, 13, 15, 16, 18, 19, 20, 22, 23, 25, 26, 28, 29, 30, 32, 33, 35, 36, 37, 39, 40, 42, 43, 45, 46, 47, 49, 50, 52, 53, 54, 56, 57, 59, 60, 61, 63, 64, 66, 67, 69, 70, 71, 73, 74, 76, 77, 78, 80, 81, 83, 84, 86, 87, 88, 90, 91, 93, 94, 95, 97, 98, 100, 101, 102, 104, 105, 107, 108

Offset: 1

Clark Kimberling, Jan 18 2011

nonn

G. C. Greubel, Table of n, a(n) for n = 1..10000

Cf. A184618, A184625.

[Floor(n*Sqrt(2) - 1/4): n in [1..100]]; // G. C. Greubel, Apr 20 2018

r=2^(1/2); h=-1/4; s=r/(r-1);
Table[Floor[n*r+h],{n,1,120}]  (* A184624 *)
Table[Floor[n*s+h-h*s],{n,1,120}]  (* A184625 *)

for(n=1, 100, print1(floor(n*sqrt(2) - 1/4), ", ")) \\ G. C. Greubel, Apr 20 2018

cp's OEIS Frontend

A184676 a(n) = n + floor((n/2-1/(4*n))^2); complement of A183867.

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