A104862 First differences of A014292.

0, 1, 1, 1, 1, 0, -2, -5, -9, -13, -15, -12, 0, 25, 65, 117, 169, 196, 158, 3, -321, -841, -1519, -2200, -2560, -2079, -79, 4121, 10881, 19720, 28638, 33435, 27351, 1547, -52895, -140772, -256000, -372775, -436655, -359763, -26871

Offset: 0

Author

Gerald McGarvey, Apr 24 2005

Keywords

• sign

Comments

Real part of the sequence of complex numbers defined by c(n) = c(n-1) + i*c(n-2) for n > 1, c(0) = 1, c(1) = 1.

a(n) = real part of the sequence b of quaternions defined by b(0)=1, b(1)=1, b(n) = b(n-1) + b(n-2)*(0,s,s,s) where s = 1/sqrt(3).

Links

• Michael De Vlieger, Table of n, a(n) for n = 0..6285

Crossrefs

Cf. A078001, A014292.

Programs

Mathematica

Differences@ LinearRecurrence[{2, -1, 0, -1}, {0, 0, 1, 2}, 42] (* Michael De Vlieger, Mar 19 2021 *)

Python

a = [0]*1000
a[1]=1
for n in range(1,55):
    print(a[n-1], end=", ")
    s=sum(a[k] for k in range(n-2))
    a[n+1] = a[n]-s
# from Alex Ratushnyak, May 03 2012

Formula

G.f.: Re(1/(1-x-ix^2)) = (1-x)/(1-2x+x^2+x^4). - Paul Barry, Apr 25 2005

a(n) = Sum_{k=0..floor(n/2)} C(n-k, k)*cos(Pi*k/2). - Paul Barry, Apr 25 2005

a(0)=0, a(1)=1, a(n+1) = a(n) - Sum_{k=0..n-3} a(k). - Alex Ratushnyak, May 03 2012