This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A186679 #18 Aug 26 2025 04:49:59
%S A186679 0,-3,4,-4,7,-14,22,-33,54,-90,145,-232,376,-611,988,-1596,2583,-4182,
%T A186679 6766,-10945,17710,-28658,46369,-75024,121392,-196419,317812,-514228,
%U A186679 832039,-1346270,2178310,-3524577,5702886,-9227466,14930353,-24157816,39088168,-63245987,102334156,-165580140
%N A186679 First differences of A116697.
%H A186679 G. C. Greubel, <a href="/A186679/b186679.txt">Table of n, a(n) for n = 0..1000</a>
%H A186679 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (-1,0,-1,1).
%F A186679 a(n) = A116697(n+1) - A116697(n).
%F A186679 a(2*n) = A128533(n).
%F A186679 a(2*n+1) = A081714(n+1).
%F A186679 a(n+2) = A075193(n+2) - a(n).
%F A186679 G.f.: x*(-3+x)/((1+x-x^2)*(1+x^2)). - _Colin Barker_, Sep 08 2012
%F A186679 From _G. C. Greubel_, Aug 24 2025: (Start)
%F A186679 a(n) = (-1)^n*Fibonacci(n+2) - (-1)^floor(n/2).
%F A186679 E.g.f.: exp(-x/2)*(cosh(p*x) - (3/sqrt(5))*sinh(p*x)) - cos(x) - sin(x), where 2*p = sqrt(5). (End)
%t A186679 Table[(-1)^n*Fibonacci[n+2] -(-1)^Floor[n/2], {n,0,40}] (* _G. C. Greubel_, Aug 24 2025 *)
%o A186679 (Magma)
%o A186679 A186679:= func< n | (-1)^n*Fibonacci(n+2) - (-1)^Floor(n/2) >;
%o A186679 [A186679(n): n in [0..40]]; // _G. C. Greubel_, Aug 24 2025
%o A186679 (SageMath)
%o A186679 def A186679(n): return (-1)**n*fibonacci(n+2) -(-1)**(n//2)
%o A186679 print([A186679(n) for n in range(41)]) # _G. C. Greubel_, Aug 24 2025
%Y A186679 Cf. A000045, A075193, A081714, A116697, A128533.
%K A186679 sign,easy,changed
%O A186679 0,2
%A A186679 _Reinhard Zumkeller_, Feb 25 2011