A062113 - OEIS

%I #21 Sep 08 2022 08:45:03

%S 1,2,3,7,10,24,34,82,116,280,396,956,1352,3264,4616,11144,15760,38048,

%T 53808,129904,183712,443520,627232,1514272,2141504,5170048,7311552,

%U 17651648,24963200,60266496,85229696,205762688,290992384,702517760

%N a(0)=1; a(1)=2; a(n) = a(n-1) + a(n-2)*(3 - (-1)^n)/2.

%C A bistable recurrence.

%H Harry J. Smith, <a href="/A062113/b062113.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,4,0,-2).

%F a(n) = a(n-1) + a(n-2) * A000034(n). - _Reinhard Zumkeller_, Jan 21 2012

%F From _Colin Barker_, Apr 20 2012: (Start)

%F a(n) = 4*a(n-2) - 2*a(n-4).

%F G.f.: (1+2*x-x^2-x^3)/(1-4*x^2+2*x^4). (End)

%t LinearRecurrence[{0,4,0,-2}, {1,2,3,7}, 40] (* _G. C. Greubel_, Oct 16 2018 *)

%o (PARI) { for (n=0, 200, if (n>1, a=a1 + a2*(3 - (-1)^n)/2; a2=a1; a1=a, if (n==0, a=a2=1, a=a1=2)); write("b062113.txt", n, " ", a) ) } \\ _Harry J. Smith_, Aug 01 2009

%o (PARI) x='x+O('x^40); Vec((1+2*x-x^2-x^3)/(1-4*x^2+2*x^4)) \\ _G. C. Greubel_, Oct 16 2018

%o (Haskell)

%o a062113 n = a062113_list !! n

%o a062113_list = 1 : 2 : zipWith (+)

%o    (tail a062113_list) (zipWith (*) a000034_list a062113_list)

%o -- _Reinhard Zumkeller_, Jan 21 2012

%o (Magma) I:=[1,2,3,7]; [n le 4 select I[n] else 4*Self(n-2) - 2*Self(n-4): n in [1..40]]; // _G. C. Greubel_, Oct 16 2018

%Y Cf. A007068, A062112.

%K easy,nonn

%O 0,2

%A _Olivier Gérard_, Jun 05 2001