A135994 - OEIS

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

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OFFSET

0,2

LINKS

Table of n, a(n) for n=0..37.

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

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)

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 *)

CROSSREFS

Cf. A000045, A000032, A135992.

Sequence in context: A262603 A131174 A291539 * A217646 A133166 A293409

Adjacent sequences: A135991 A135992 A135993 * A135995 A135996 A135997

KEYWORD

sign,easy

AUTHOR

Paul Curtz, Mar 03 2008

EXTENSIONS

More terms from Colin Barker, Feb 02 2013

STATUS

approved