|
%I #22 May 10 2020 04:27:37
%S 0,1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0,1,1,1,
%T 1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,
%U 0,0,0,1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0
%N Expansion of x/(1 - x + x^5 - x^6).
%C A transformation of the Fibonacci numbers: a(n) = A112712(n) mod 2.
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,-1,1).
%F G.f.: x/(1 - x + x^5 - x^6).
%F a(n) = a(n-1) - a(n-5) + a(n-6).
%F a(n) = a(n-10).
%F a(n) = (Sum_{k=0..floor((n+2)/2)} (-1)^(k+1)*C(n-k+2, k-1)*F(n-2*k+2)) mod 2.
%t CoefficientList[Series[x/(1 - x + x^5 - x^6), {x, 0, 100}], x] (* or *) LinearRecurrence[{1, 0, 0, 0, -1, 1}, {0, 1, 1, 1, 1, 1}, 100] (* _Harvey P. Dale_, Feb 16 2014 *)
%Y Cf. A000035, A133872, A088911, A131078.
%K nonn,easy
%O 0,1
%A _Paul Barry_, Sep 15 2005
%E Incorrect g.f. removed by _Georg Fischer_, May 15 2019
|
