A168397 a(n) = 8 * floor(n/2).

0, 8, 8, 16, 16, 24, 24, 32, 32, 40, 40, 48, 48, 56, 56, 64, 64, 72, 72, 80, 80, 88, 88, 96, 96, 104, 104, 112, 112, 120, 120, 128, 128, 136, 136, 144, 144, 152, 152, 160, 160, 168, 168, 176, 176, 184, 184, 192, 192, 200, 200, 208, 208, 216, 216, 224, 224, 232, 232, 240, 240, 248

Offset: 1

Author

Vincenzo Librandi, Nov 24 2009

Keywords

• nonn
• easy
• less

Comments

a(n+1) is the total number of unit circles (on square lattice) enclosing a circle of radius n centered at (0,0), with intersections allowed. If intersections are prohibited the sequence would be {a(n+2)}. See illustration in links. - Kival Ngaokrajang, Jun 21 2014

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• Kival Ngaokrajang, Illustration of initial terms
• Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

Crossrefs

Cf. A004526.

Programs

Magma

[8*Floor(n/2): n in [1..70]]; // Vincenzo Librandi, Sep 18 2013

Maple

A168397:=n->8*floor(n/2); seq(A168397(n), n=1..50); # Wesley Ivan Hurt, Jun 21 2014

Mathematica

Table[8 Floor[n/2], {n, 70}] (* Vincenzo Librandi, Sep 18 2013 *)

Formula

a(n) = 8*n - a(n-1) - 8, with n>1, a(1)=0.

G.f.: 8*x^2/((1+x)*(x-1)^2). - Vincenzo Librandi, Sep 18 2013

a(n) = 8 * floor(n/2) = 8 * A004526(n). - Vincenzo Librandi, Sep 18 2013

E.g.f.: 2*(1 + (2*x - 1)*exp(2*x))*exp(-x). - G. C. Greubel, Jul 19 2016

Extensions

Simpler definition and terms corrected by Vincenzo Librandi, Sep 18 2013