cp's OEIS Frontend

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.

A135994 First differences of A135992.

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%I A135994 #19 Sep 27 2016 18:36:55
%S A135994 0,2,-1,6,-3,16,-8,42,-21,110,-55,288,-144,754,-377,1974,-987,5168,
%T A135994 -2584,13530,-6765,35422,-17711,92736,-46368,242786,-121393,635622,
%U A135994 -317811,1664080,-832040,4356618,-2178309,11405774,-5702887,29860704,-14930352,78176338
%N A135994 First differences of A135992.
%H A135994 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,3,0,-1).
%F A135994 a(n) = 3*a(n-2) - a(n-4) for n>3. G.f.: -x*(x-2) / ((x^2-x-1)*(x^2+x-1)). [_Colin Barker_, Feb 02 2013]
%F A135994 From _Vladimir Reshetnikov_, Sep 24 2016: (Start)
%F A135994 a(n) = Sum_{k=1..n} (-1)^(k+1) * Fibonacci(k) * Lucas(n-k).
%F A135994 a(n) = (Lucas(n) - (-1)^n * Fibonacci(n+3))/2, where Fibonacci(n) = A000045(n), Lucas(n) = A000032(n). (End)
%t A135994 Differences[Flatten[{Last[#],First[#]}&/@Partition[Fibonacci[ Range[ 40]],2]]] (* or *) LinearRecurrence[{0,3,0,-1},{0,2,-1,6},40] (* _Harvey P. Dale_, Sep 16 2013 *)
%t A135994 Table[(LucasL[n] - (-1)^n Fibonacci[n + 3])/2, {n, 0, 40}] (* _Vladimir Reshetnikov_, Sep 24 2016 *)
%Y A135994 Cf. A000045, A000032, A135992.
%K A135994 sign,easy
%O A135994 0,2
%A A135994 _Paul Curtz_, Mar 03 2008
%E A135994 More terms from _Colin Barker_, Feb 02 2013