OFFSET
0,2
COMMENTS
Binomial transform of 1,1,8,1,8,1,8,1,8,1,8,1,8,1,8,...
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,-2).
FORMULA
a(n) = 3*a(n-1) - 2*a(n-2), n>2, with a(0)=1, a(1)=2, a(2)=11.
a(n) = 9*2^(n-1) - 7, n>0, with a(0)=1.
a(n) = 2*a(n-1) + 7, n>1, with a(0)=1, a(1)=2.
From G. C. Greubel, Sep 08 2016: (Start)
a(n) = 9*2^(n-1) - 7 for n >= 1.
E.g.f.: (1/2)*(9*exp(2*x) - 14*exp(x) + 7). (End)
MATHEMATICA
Join[{1}, LinearRecurrence[{3, -2}, {2, 11}, 25]] (* or *) Join[{1}, Table[9*2^(n-1) - 7, {n, 1, 25}]] (* G. C. Greubel, Sep 08 2016 *)
PROG
(PARI) Vec((1-x+7*x^2)/((1-x)*(1-2*x))+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Philippe Deléham, Jan 05 2009
STATUS
approved