OFFSET
0,3
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (4,12).
FORMULA
16*a(n) = 3*6^n +(-1)^n*2^n, n>0. - R. J. Mathar, Sep 03 2013
From G. C. Greubel, Mar 01 2021: (Start)
a(n) = (6^(n+1) - (-2)^(n+1))/32 + (3/4)*[n=0].
E.g.f.: (exp(-2*x) + 3*exp(6*x))/16. (End)
MATHEMATICA
LinearRecurrence[{4, 12}, {1, 1, 7}, 40] (* G. C. Greubel, Mar 01 2021 *)
PROG
(SageMath) [1]+[(6^(n+1) - (-2)^(n+1))/32 for n in [1..40]] # G. C. Greubel, Mar 01 2021
(Magma) [n eq 0 select 1 else (6^(n+1) -(-2)^(n+1))/32: n in [0..40]]; // G. C. Greubel, Mar 01 2021
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Philippe Deléham, Jan 18 2009
STATUS
approved