A179207 a(n) = n - 1 + ceiling((-3 + n^2)/2) if n > 1 with a(1)=1, complement of A182835.

1, 2, 5, 10, 15, 22, 29, 38, 47, 58, 69, 82, 95, 110, 125, 142, 159, 178, 197, 218, 239, 262, 285, 310, 335, 362, 389, 418, 447, 478, 509, 542, 575, 610, 645, 682, 719, 758, 797, 838, 879, 922, 965, 1010, 1055, 1102, 1149, 1198, 1247, 1298, 1349, 1402, 1455

Offset: 1

Author

Clark Kimberling, Jan 07 2011

Keywords

• nonn
• easy

Links

• Guenther Schrack, Table of n, a(n) for n = 1..10010
• Index entries for linear recurrences with constant coefficients, signature (2,0,-2,1).

Crossrefs

Cf. A182835, A047838.

First differences: A109613(n) for n > 2. - Guenther Schrack, Jun 06 2018

Programs

GAP

a:=[2,5,10,15];; for n in [5..60] do a[n]:=2*a[n-1]-2*a[n-3]+a[n-4]; od; a:=Concatenation([1],a); # Muniru A Asiru, Aug 05 2018

Maple

a:=n->n-1+ceil((-3+n^2)/2): 1,seq(a(n),n=2..60); # Muniru A Asiru, Aug 05 2018

Mathematica

Table[n-1+Ceiling[(n*n-3)/2], {n,60}] (* Vladimir Joseph Stephan Orlovsky, Apr 02 2011 *)
Join[{1},LinearRecurrence[{2,0,-2,1},{2,5,10,15},52]] (* Ray Chandler, Jul 15 2015 *)

Formula

a(n) = n - 1 + ceiling((-3 + n^2)/2) if n > 1.

a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4). - Joerg Arndt, Apr 02 2011

From Guenther Schrack, Jun 06 2018: (Start)

a(n) = (2*n^2 + 4*n - 9 + (-1)^n)/4 for n > 1.

a(n) = a(n-2) + 2*n for n > 3.

a(-n) = a(n-2) for n > 1.

a(n) = n - 1 + A047838(n) for n > 1. (End)

G.f.: x * (1 + x^2 + 2*x^3 - 2*x^4) / (1 - 2*x + 2*x^3 - x^4). - Michael Somos, Oct 28 2018

Sum_{n>=1} 1/a(n) = 8/3 + tan(sqrt(5)*Pi/2)*Pi/(2*sqrt(5)) - cot(sqrt(3/2)*Pi)*Pi/(2*sqrt(6)). - Amiram Eldar, Sep 16 2022