A186679 First differences of A116697.

0, -3, 4, -4, 7, -14, 22, -33, 54, -90, 145, -232, 376, -611, 988, -1596, 2583, -4182, 6766, -10945, 17710, -28658, 46369, -75024, 121392, -196419, 317812, -514228, 832039, -1346270, 2178310, -3524577, 5702886, -9227466, 14930353, -24157816, 39088168, -63245987, 102334156, -165580140

Offset: 0

Author

Reinhard Zumkeller, Feb 25 2011

Keywords

• sign
• easy
• changed

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (-1,0,-1,1).

Crossrefs

Cf. A000045, A075193, A081714, A116697, A128533.

Programs

Magma

A186679:= func< n | (-1)^n*Fibonacci(n+2) - (-1)^Floor(n/2) >;
[A186679(n): n in [0..40]]; // G. C. Greubel, Aug 24 2025

Mathematica

Table[(-1)^n*Fibonacci[n+2] -(-1)^Floor[n/2], {n,0,40}] (* G. C. Greubel, Aug 24 2025 *)

SageMath

def A186679(n): return (-1)**n*fibonacci(n+2) -(-1)**(n//2)
print([A186679(n) for n in range(41)]) # G. C. Greubel, Aug 24 2025

Formula

a(n) = A116697(n+1) - A116697(n).

a(2*n) = A128533(n).

a(2*n+1) = A081714(n+1).

a(n+2) = A075193(n+2) - a(n).

G.f.: x*(-3+x)/((1+x-x^2)*(1+x^2)). - Colin Barker, Sep 08 2012

From G. C. Greubel, Aug 24 2025: (Start)

a(n) = (-1)^n*Fibonacci(n+2) - (-1)^floor(n/2).

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)