OFFSET
0,1
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (12,-33).
FORMULA
a(n) = ((4+sqrt(3))*(6+sqrt(3))^n + (4-sqrt(3))*(6-sqrt(3))^n)/2.
G.f.: (4-21*x)/(1-12*x+33*x^2).
E.g.f.: (4*cosh(sqrt(3)*x) + sqrt(3)*sinh(sqrt(3)*x))*exp(6*x). - G. C. Greubel, Sep 13 2017
MATHEMATICA
LinearRecurrence[{12, -33}, {4, 27}, 50] (* or *) CoefficientList[Series[(4 - 21*x)/(1 - 12*x + 33*x^2), {x, 0, 50}], x] (* G. C. Greubel, Sep 13 2017 *)
PROG
(Magma) [ n le 2 select 23*n-19 else 12*Self(n-1)-33*Self(n-2): n in [1..20] ];
(PARI) x='x+O('x^50); Vec((4-21*x)/(1-12*x+33*x^2)) \\ G. C. Greubel, Sep 13 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Klaus Brockhaus, Aug 12 2009
STATUS
approved