A168398 - OEIS

%I #33 Mar 19 2024 09:34:13

%S 4,4,12,12,20,20,28,28,36,36,44,44,52,52,60,60,68,68,76,76,84,84,92,

%T 92,100,100,108,108,116,116,124,124,132,132,140,140,148,148,156,156,

%U 164,164,172,172,180,180,188,188,196,196,204,204,212,212,220,220,228,228

%N a(n) = 4 + 8*floor((n-1)/2).

%H Vincenzo Librandi, <a href="/A168398/b168398.txt">Table of n, a(n) for n = 1..1000</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)=4.

%F G.f.: 4*x*(1 + x^2)/((1+x)*(x-1)^2). - _Vincenzo Librandi_, Sep 18 2013

%F a(n) = a(n-1) +a(n-2) -a(n-3). - _Vincenzo Librandi_, Sep 18 2013

%F a(n) = 4 * A109613(n-1). - _Bruno Berselli_, Sep 18 2013

%F E.g.f.: 4*(1 + (x - 1)*cosh(x) + x*sinh(x)). - _G. C. Greubel_, Jul 20 2016

%t Table[4 + 8*Floor[(n - 1)/2], {n, 60}] (* _Vincenzo Librandi_, Sep 18 2013 *)

%t LinearRecurrence[{1,1,-1},{4,4,12},60] (* or *) With[{r=NestList[ #+8&,4,30]},Riffle[r,r]] (* _Harvey P. Dale_, Oct 18 2021 *)

%o (Magma) [4+8*Floor((n-1)/2): n in [1..70]]; // _Vincenzo Librandi_, Sep 18 2013

%Y Cf. A017113, A109613.

%K nonn,easy,less

%O 1,1

%A _Vincenzo Librandi_, Nov 25 2009

%E New definition by _Vincenzo Librandi_, Sep 18 2013