|
%I #25 Sep 08 2022 08:45:55
%S 1,0,-1,-4,-12,-33,-88,-232,-609,-1596,-4180,-10945,-28656,-75024,
%T -196417,-514228,-1346268,-3524577,-9227464,-24157816,-63245985,
%U -165580140,-433494436,-1134903169,-2971215072,-7778742048,-20365011073,-53316291172,-139583862444
%N a(n) = 0^n + 1 - F(n-1)^2 - F(n)^2, where F = A000045.
%C Row sums of number triangle A186024.
%H G. C. Greubel, <a href="/A186025/b186025.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (4,-4,1).
%F G.f.: (1-4x+3x^2-x^3)/(1-4x+4x^2-x^3) = (1-4x+3x^2-x^3)/((1-x)(1-3x+x^2)).
%F a(n) = -A027941(n-1), n>0. - _R. J. Mathar_, Mar 21 2013
%t Join[{1}, Table[0^n + 1 - Fibonacci[n - 1]^2 - Fibonacci[n]^2, {n, 30}]] (* _Vincenzo Librandi_, Apr 24 2015 *)
%t LinearRecurrence[{4,-4,1},{1,0,-1,-4},30] (* _Harvey P. Dale_, Dec 16 2015 *)
%o (Magma) [0^n+1-Fibonacci(n-1)^2-Fibonacci(n)^2: n in [0..30]]; // _Vincenzo Librandi_, Apr 24 2015
%o (PARI) x='x+O('x^50); Vec((1-4*x+3*x^2-x^3)/(1-4*x+4*x^2-x^3)) \\ _G. C. Greubel_, Jul 24 2017
%Y Cf. A000045, A027941.
%K sign,easy
%O 0,4
%A _Paul Barry_, Feb 10 2011
%E More terms from _Vincenzo Librandi_, Apr 24 2015
|
