OFFSET
0,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
Index entries for linear recurrences with constant coefficients, signature (1,2).
FORMULA
a(n) = A084214(n+2) for n > 0.
a(n) = a(n-1) + 2*a(n-2) for n > 2; a(0) = 1, a(1) = 6, a(2) = 14.
G.f.: (1+2*x)*(1+3*x)/((1+x)*(1-2*x)).
E.g.f.: (1/3)*(10*exp(2*x) - 9 + 2*exp(-x)). - G. C. Greubel, Jul 28 2016
MATHEMATICA
{1}~Join~Table[(10*2^n + 2*(-1)^n)/3, {n, 40}] (* or *)
{1}~Join~LinearRecurrence[{1, 2}, {6, 14}, 40] (* G. C. Greubel, Jul 28 2016 *)
PROG
(Magma) [1] cat [ (10*2^n+2*(-1)^n)/3: n in [1..30] ];
(PARI) a(n) = if(n, (10<<n + 2*(-1)^n)/3, 1) \\ Charles R Greathouse IV, Jul 29 2016
(Sage) [1]+[(10*2^n +2*(-1)^n)/3 for n in (1..40)] # G. C. Greubel, Feb 05 2021
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Klaus Brockhaus, Dec 01 2009
STATUS
approved