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.
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
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
KEYWORD
nonn,easy,less
AUTHOR
Vincenzo Librandi, Nov 24 2009
EXTENSIONS
Simpler definition and terms corrected by Vincenzo Librandi, Sep 18 2013
STATUS
approved