A135994 First differences of A135992.

0, 2, -1, 6, -3, 16, -8, 42, -21, 110, -55, 288, -144, 754, -377, 1974, -987, 5168, -2584, 13530, -6765, 35422, -17711, 92736, -46368, 242786, -121393, 635622, -317811, 1664080, -832040, 4356618, -2178309, 11405774, -5702887, 29860704, -14930352, 78176338

Offset: 0

Author

Paul Curtz, Mar 03 2008

Keywords

• sign
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (0,3,0,-1).

Crossrefs

Cf. A000045, A000032, A135992.

Programs

Mathematica

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 *)
Table[(LucasL[n] - (-1)^n Fibonacci[n + 3])/2, {n, 0, 40}] (* Vladimir Reshetnikov, Sep 24 2016 *)

Formula

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]

From Vladimir Reshetnikov, Sep 24 2016: (Start)

a(n) = Sum_{k=1..n} (-1)^(k+1) * Fibonacci(k) * Lucas(n-k).

a(n) = (Lucas(n) - (-1)^n * Fibonacci(n+3))/2, where Fibonacci(n) = A000045(n), Lucas(n) = A000032(n). (End)

Extensions

More terms from Colin Barker, Feb 02 2013