OFFSET
0,2
COMMENTS
Fourth binomial transform of A016116.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (8,-14).
FORMULA
a(n) = ((2+sqrt(2))*(4+sqrt(2))^n+(2-sqrt(2))*(4-sqrt(2))^n)/4.
a(n) = 8*a(n-1)-14*a(n-2). - R. J. Mathar, Jun 18 2009
MATHEMATICA
CoefficientList[Series[(1-3x)/(1-8x+14x^2), {x, 0, 30}], x] (* or *) LinearRecurrence[{8, -14}, {1, 5}, 30] (* Harvey P. Dale, Feb 29 2024 *)
PROG
(PARI) F=nfinit(x^2-2); for(n=0, 20, print1(nfeltdiv(F, ((2+x)*(4+x)^n+(2-x)*(4-x)^n), 4)[1], ", ")) \\ Klaus Brockhaus, Jun 19 2009
(Magma)[Floor(((2+Sqrt(2))*(4+Sqrt(2))^n+(2-Sqrt(2))*(4-Sqrt(2))^n)/4): n in [0..30]]; // Vincenzo Librandi, Aug 18 2011
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Al Hakanson (hawkuu(AT)gmail.com), Jun 17 2009
EXTENSIONS
Extended by R. J. Mathar and Klaus Brockhaus, Jun 18 2009
Edited by Klaus Brockhaus, Jul 05 2009
STATUS
approved