A173388 - OEIS

%I #13 Oct 03 2018 16:10:27

%S 1,1,1,1,2,2,2,4,4,6,6,10,10,16,16,26,26,42,42,68,68,110,110,178,178,

%T 288,288,466,466,754,754,1220,1220,1974,1974,3194,3194,5168,5168,8362,

%U 8362,13530,13530,21892,21892,35422,35422,57314,57314,92736,92736

%N a(n) = a(n - 3) + a(n - 4) if n is even, else a(n - 2) + a(n - 3).

%C The sequence is designed so that all the numbers, see A055389 or A006355, except the first two appear twice.

%C The limiting ratio a(n+1)/a(n) alternates between the golden ratio and one.

%C Essentially the same as A214927 (except for the first 4 terms and the offset). - _Georg Fischer_, Oct 01 2018

%F a(n) = a(n-2)+a(n-4), n > 7.

%F G.f.: (x^7+1+x-x^6)/(1-x^2-x^4).

%t a[0] = 1; a[1] = 1; a[2] = 1; a[3] = 1;

%t a[n_] := a[n] = If[Mod[n, 2] == 0, a[n - 3] + a[n - 4], a[n - 2] + a[n - 3]];

%t Table[a[n], {n, 0, 50}]

%K nonn,easy,less

%O 0,5

%A _Roger L. Bagula_, Feb 17 2010

%E Formula added by the Assoc. Editors of the OEIS, Feb 24 2010