A168390 - OEIS

%I #33 Mar 04 2024 01:12:26

%S 1,9,9,17,17,25,25,33,33,41,41,49,49,57,57,65,65,73,73,81,81,89,89,97,

%T 97,105,105,113,113,121,121,129,129,137,137,145,145,153,153,161,161,

%U 169,169,177,177,185,185,193,193,201,201,209,209,217,217,225,225,233,233

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

%H Vincenzo Librandi, <a href="/A168390/b168390.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) - 6, with n>1, a(1)=1.

%F a(1)=1, a(2)=9, a(3)=9; for n>3, a(n) = a(n-1) + a(n-2) - a(n-3). - _Harvey P. Dale_, Jul 28 2012

%F G.f.: x*(1 + 8*x - x^2)/((1+x)*(x-1)^2). - _Vincenzo Librandi_, Sep 18 2013

%F a(n) = A168381(n) - 1 = A168378(n) - 2. - _Bruno Berselli_, Sep 18 2013

%F E.g.f.: (2 - exp(x) + (4*x - 1)*exp(2*x))*exp(-x). - _G. C. Greubel_, Jul 19 2016

%t RecurrenceTable[{a[1]==1,a[n]==8n-a[n-1]-6},a,{n,60}] (* or *) LinearRecurrence[{1,1,-1},{1,9,9},60] (* or *) With[{c=Table[8n+1,{n,0,40}]},Rest[Riffle[c,c]]] (* _Harvey P. Dale_, Jul 28 2012 *)

%t Table[1 + 8 Floor[n/2], {n, 60}] (* _Bruno Berselli_, Sep 18 2013 *)

%t CoefficientList[Series[(1 + 8 x - x^2)/((1 + x) (x - 1)^2), {x, 0, 70}], x] (* _Vincenzo Librandi_, Sep 18 2013 *)

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

%Y Cf. A017077, A168378, A168381.

%K nonn,easy

%O 1,2

%A _Vincenzo Librandi_, Nov 24 2009

%E New definition by _Vincenzo Librandi_, Sep 18 2013