OFFSET
0,3
COMMENTS
Binomial transform of A083884.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
Index entries for linear recurrences with constant coefficients, signature (4,4,-16).
FORMULA
a(n) = (4^n+2^n+0^n+(-2)^n)/4.
G.f.: (4*x^3-2*x^2-3*x+1)/((2*x+1)*(2*x-1)*(4*x-1)).
E.g.f.: exp(4*x)+exp(2*x)+exp(0)+exp(-2*x).
a(0)=1, a(1)=1, a(2)=6, a(3)=16, a(n)=4*a(n-1)+4*a(n-2)-16*a(n-3) [From Harvey P. Dale, Dec 12 2011]
MATHEMATICA
Join[{1}, Table[(4^n+2^n+(-2)^n)/4, {n, 30}]] (* or *) Join[{1}, LinearRecurrence[ {4, 4, -16}, {1, 6, 16}, 30]] (* Harvey P. Dale, Dec 12 2011 *)
PROG
(Magma) [(4^n+2^n+0^n+(-2)^n)/4: n in [0..20]]; // Vincenzo Librandi, Jun 16 2011
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, May 09 2003
STATUS
approved