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
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jan 19 2011
STATUS
approved