OFFSET
0,4
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..500
Index entries for linear recurrences with constant coefficients, signature (3,6,-8).
FORMULA
a(n) = (4^n - 2 + (-2)^n)/18.
G.f.: x^2/((1-x)*(1+2*x)*(1-4*x)).
a(n) = 3*a(n-1) + 6*a(n-2) - 8*a(n-3).
E.g.f.: (exp(2*x) - exp(-x))^2/18 = (exp(4*x) - 2*exp(x) + exp(-x))/18.
Binomial transform of 0, 0, 1, 0, 9, 0, 81, ... .
a(n) = floor(2^n/3)ceiling(2^n/3)/2. - Paul Barry, Apr 28 2004
MATHEMATICA
Join[{a=0, b=0}, Table[c=2*b+8*a+1; a=b; b=c, {n, 60}]] (* Vladimir Joseph Stephan Orlovsky, Feb 05 2011*)
LinearRecurrence[{3, 6, -8}, {0, 0, 1}, 30] (* Harvey P. Dale, Nov 11 2011 *)
PROG
(Magma) [(4^n-2+(-2)^n)/18: n in [0..35]]; // Vincenzo Librandi, Jul 05 2011
(SageMath) [(4^n-2+(-2)^n)/18 for n in range(41)] # G. C. Greubel, Oct 11 2022
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, May 16 2003
STATUS
approved