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

1,2

Comments

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

Links

Nathaniel Johnston, Table of n, a(n) for n = 1..5000

Index entries for linear recurrences with constant coefficients, signature (2,0,-2,1).

Formula

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

Maple

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

Mathematica

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, 55}]. (* Fred Daniel Kline, Jun 24 2016 *)

Prog

(PARI) a(n) = n+floor((n/2-1/(4*n))^2); \\ Michel Marcus, Dec 09 2015
(Magma) [n+Floor((n/2-1/(4*n))^2): n in [1..60]]; // Vincenzo Librandi, Dec 09 2015

Crossrefs

Cf. A183867, A184625, A198442.

Sequence in context: A133436 A363244 A351897 * A191175 A191125 A001225

Adjacent sequences: A184673 A184674 A184675 * A184677 A184678 A184679

Keyword

nonn,easy

Author

Clark Kimberling, Jan 19 2011

Status

approved