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A117616 a(0)=0, a(n)=4a(n-1)+2 for n odd, a(n)=4a(n-1) for n even.

%I A117616 #17 Mar 10 2023 17:49:14
%S A117616 0,2,8,34,136,546,2184,8738,34952,139810,559240,2236962,8947848,
%T A117616 35791394,143165576,572662306,2290649224,9162596898,36650387592,
%U A117616 146601550370,586406201480,2345624805922,9382499223688,37529996894754
%N A117616 a(0)=0, a(n)=4a(n-1)+2 for n odd, a(n)=4a(n-1) for n even.
%D A117616 L. Rosenfeld, Nuclear Forces, section II, Interscience, New York, 1948, p 202
%H A117616 Harvey P. Dale, <a href="/A117616/b117616.txt">Table of n, a(n) for n = 0..1000</a>
%H A117616 <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (4,1,-4).
%F A117616 a(n) = (-5-3*(-1)^n+2^(3+2*n))/15. a(n) = 4*a(n-1)+a(n-2)-4*a(n-3). G.f.: 2*x / ((x-1)*(x+1)*(4*x-1)). [_Colin Barker_, Feb 17 2013]
%F A117616 a(n) = 2*A033114(n). - _R. J. Mathar_, Feb 27 2019
%p A117616 a:=proc(n) if n=0 then 0 elif n mod 2 = 1 then 4*a(n-1)+2 else 4*a(n-1) fi end: seq(a(n),n=0..23);
%t A117616 b[0] := 0 b[1] := 2 b[n_?EvenQ] := b[n] = 4*b[n - 1] b[n_?OddQ] := b[n] = 4*b[n - 1] + 2 a = Table[b[n], {n, 0, 25}]
%t A117616 nxt[{n_,a_}]:={n+1,If[EvenQ[n],4a+2,4a]}; NestList[nxt,{0,0},30][[;;,2]] (* or *) LinearRecurrence[{4,1,-4},{0,2,8},30] (* _Harvey P. Dale_, Mar 10 2023 *)
%K A117616 nonn,easy
%O A117616 0,2
%A A117616 _Roger L. Bagula_, Apr 07 2006
%E A117616 Edited by _N. J. A. Sloane_, Apr 16 2006