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A168397 a(n) = 8 * floor(n/2). 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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).

FORMULA

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

a(n) = 4*n + 2*(-1)^n - 2. - Paolo P. Lava, Nov 27 2009

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

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 *)

PROG

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

CROSSREFS

Cf. A004526.

Sequence in context: A040057 A205709 A028997 * A186986 A112439 A309461

Adjacent sequences:  A168394 A168395 A168396 * A168398 A168399 A168400

KEYWORD

nonn,easy,less

AUTHOR

Vincenzo Librandi, Nov 24 2009

EXTENSIONS

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

STATUS

approved

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Last modified October 19 16:17 EDT 2019. Contains 328223 sequences. (Running on oeis4.)