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Floor(Fibonacci(2n+1)/9).
0

%I #7 Jun 06 2016 14:41:49

%S 0,0,0,1,3,9,25,67,177,464,1216,3184,8336,21824,57136,149585,391619,

%T 1025273,2684201,7027331,18397793,48166048,126100352,330135008,

%U 864304672,2262779008,5924032352,15509318049,40603921795,106302447337,278303420217

%N Floor(Fibonacci(2n+1)/9).

%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (4, -4, 1, 0, 0, -1, 4, -4, 1).

%F a(n) = ( A000045(2n+1)-A154811(n) )/9 = floor(A122367(n)/9) = floor(A001519(n+1)/9) = floor( |A099496(n)|/9).

%F a(n)=3a(n-1)-a(n-2)+|A112690(n+10)|, i.e., a(n)-3a(n-1)+a(n-2) is a sequence of period 12 containing 0's and 1's. - _R. J. Mathar_, Feb 23 2009

%F G.f.: (1-x+x^2)/((1-x)(1+x^2)(1-3x+x^2)(1-x^2+x^4)). - _R. J. Mathar_, Feb 23 2009

%t Floor[Fibonacci[2*Range[0,30]+1]/9] (* or *) LinearRecurrence[{4,-4,1,0,0,-1,4,-4,1},{0,0,0,1,3,9,25,67,177},31] (* _Harvey P. Dale_, Jun 06 2016 *)

%Y Cf. A069403.

%K nonn

%O 0,5

%A _Paul Curtz_, Feb 10 2009

%E Edited and extended by _R. J. Mathar_, Jan 23 2009, Feb 23 2009