OFFSET
3,2
REFERENCES
S. Mukai, An Introduction to Invariants and Moduli, Cambridge, 2003; see p. 483.
LINKS
Chai Wah Wu, Table of n, a(n) for n = 3..3324
Index entries for linear recurrences with constant coefficients, signature (0,7,0,-14,0,8).
FORMULA
a(n) = 7*a(n-2) - 14*a(n-4) + 8*a(n-6) for n > 8. - Chai Wah Wu, Jun 19 2016
G.f.: x^3*(1 + 2*x - 2*x^2 - 10*x^3 + 8*x^5)/(1 - 7*x^2 + 14*x^4 - 8*x^6). - Chai Wah Wu, Jun 19 2016
a(n) = (3*(1 + (-1)^n)*2^(n/2) - (1 - (-1)^n)*(2 - 2^n))/12. - Colin Barker, Mar 26 2019
a(n) = (2^n - 2)/6 if n is odd else 2^(n/2 - 1). - Peter Luschny, Mar 26 2019
MATHEMATICA
Table[(3 (1 + (-1)^n) 2^(n/2) - (1 - (-1)^n) (2 - 2^n))/12, {n, 3, 50}] (* Bruno Berselli, Mar 26 2019 *)
PROG
(PARI) Vec(x^3*(1 + 2*x - 2*x^2 - 10*x^3 + 8*x^5) / ((1 - x)*(1 + x)*(1 - 2*x)*(1 + 2*x)*(1 - 2*x^2)) + O(x^40)) \\ Colin Barker, Mar 26 2019
(Sage)
def a(n): return (2^n-2)//6 if is_odd(n) else 2^(n//2-1))
print([a(n) for n in (3..41)]) # Peter Luschny, Mar 26 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Jun 10 2005
EXTENSIONS
More terms from Chai Wah Wu, Jun 19 2016
STATUS
approved