OFFSET
0,7
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
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
MATHEMATICA
Differences@ LinearRecurrence[{2, -1, 0, -1}, {0, 0, 1, 2}, 42] (* Michael De Vlieger, Mar 19 2021 *)
PROG
(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
CROSSREFS
KEYWORD
sign
AUTHOR
Gerald McGarvey, Apr 24 2005
STATUS
approved