OFFSET
0,4
COMMENTS
Binomial transform of A084150. - Paul Barry, May 16 2003
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (6,-4,-8).
FORMULA
a(n) = ((2+sqrt(8))^n+(2-sqrt(8))^n-2^(n+1))/16; E.g.f. : exp(2x)(sinh(sqrt(2)x))^2/4=(exp(x)sinh(sqrt(2)x)/sqrt(2))^2/2. - Paul Barry, May 16 2003
G.f.: x^2/((1-2*x)*(1-4*x-4*x^2)). - Bruno Berselli, Aug 20 2011
MATHEMATICA
LinearRecurrence[{6, -4, -8}, {0, 0, 1}, 30] (* Harvey P. Dale, Jul 15 2014 *)
Table[2^(n-4)*(LucasL[n, 2] - 2), {n, 0, 20}] (* Vladimir Reshetnikov, Oct 07 2016 *)
PROG
(Magma) [Floor(((2+Sqrt(8))^n+(2-Sqrt(8))^n-2^(n+1))/16): n in [0..30] ]; // Vincenzo Librandi, Aug 20 2011
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved