%I #13 Jan 01 2024 11:07:15
%S 0,1,2,4,10,18,46,82,210,374,958,1706,4370,7782,19934,35498,90930,
%T 161926,414782,738634,1892050,3369318,8630686,15369322,39369330,
%U 70107974,179585278,319801226,819187730,1458790182,3736768094
%N a(n) = 5a(n-2) - 2a(n-4).
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,5,0,-2).
%F Also a(n) = a(n-1) + 2a(n-2) if n is odd, else a(n) = 2a(n-1) + a(n-2).
%F a(2n) = 2*A005824(2n), a(2n+1) = A005824(2n) + A005824(2n+1).
%F G.f.: x*(1+2*x-x^2)/(1-5*x^2+2*x^4).
%t a[0] = 0; a[1] = 1; a[n_] := a[n] = If[ OddQ[n], a[n - 1] + 2a[n - 2], 2a[n - 1] + a[n - 2]]; Table[a[n], {n, 0, 30}]
%t LinearRecurrence[{0,5,0,-2},{0,1,2,4},40] (* _Harvey P. Dale_, Jul 05 2022 *)
%Y Cf. A005824. a(2n+1) = A052913(n).
%K nonn
%O 0,3
%A _Robert G. Wilson v_, Dec 29 2002
%E Corrected the g.f. and index in formula with A052913 _R. J. Mathar_, Apr 01 2009, May 02 2009