OFFSET
1,2
COMMENTS
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (0,3).
FORMULA
a(n) = (4 + (-1)^n) * 3^((2*n - 5 + (-1)^n)/4).
G.f.: x*(1+5*x)/(1-3*x^2).
a(n) = A162813(n-1), for n >= 2.
From G. C. Greubel, Jul 27 2024: (Start)
a(n) = (1/6)*3^(n/2)*( 5*(1+(-1)^n) + sqrt(3)*(1-(-1)^n) ).
E.g.f.: (1/3)*(sqrt(3)*sinh(sqrt(3)*x) + 10*(sinh(sqrt(3)*x/2))^2). (End)
MATHEMATICA
LinearRecurrence[{0, 3}, {1, 5}, 41] (* G. C. Greubel, Jul 27 2024 *)
PROG
(Magma) [ n le 2 select 4*n-3 else 3*Self(n-2): n in [1..35] ];
(SageMath) [3^(n/2)*(5*((n+1)%2) +sqrt(3)*(n%2))/3 for n in range(1, 41)] # G. C. Greubel, Jul 27 2024
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Klaus Brockhaus, Oct 14 2009
STATUS
approved