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%I #32 Mar 19 2024 09:34:09
%S 0,8,8,16,16,24,24,32,32,40,40,48,48,56,56,64,64,72,72,80,80,88,88,96,
%T 96,104,104,112,112,120,120,128,128,136,136,144,144,152,152,160,160,
%U 168,168,176,176,184,184,192,192,200,200,208,208,216,216,224,224,232,232,240,240,248
%N a(n) = 8 * floor(n/2).
%C 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
%H Vincenzo Librandi, <a href="/A168397/b168397.txt">Table of n, a(n) for n = 1..1000</a>
%H Kival Ngaokrajang, <a href="/A168397/a168397.pdf">Illustration of initial terms</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).
%F a(n) = 8*n - a(n-1) - 8, with n>1, a(1)=0.
%F G.f.: 8*x^2/((1+x)*(x-1)^2). - _Vincenzo Librandi_, Sep 18 2013
%F a(n) = 8 * floor(n/2) = 8 * A004526(n). - _Vincenzo Librandi_, Sep 18 2013
%F E.g.f.: 2*(1 + (2*x - 1)*exp(2*x))*exp(-x). - _G. C. Greubel_, Jul 19 2016
%p A168397:=n->8*floor(n/2); seq(A168397(n), n=1..50); # _Wesley Ivan Hurt_, Jun 21 2014
%t Table[8 Floor[n/2], {n, 70}] (* _Vincenzo Librandi_, Sep 18 2013 *)
%o (Magma) [8*Floor(n/2): n in [1..70]]; // _Vincenzo Librandi_, Sep 18 2013
%Y Cf. A004526.
%K nonn,easy,less
%O 1,2
%A _Vincenzo Librandi_, Nov 24 2009
%E Simpler definition and terms corrected by _Vincenzo Librandi_, Sep 18 2013