OFFSET
0,2
COMMENTS
Binomial transform of 1,1,9,1,9,1,9,1,9,1,9,1,9,1,9,...
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)=12.
a(n) = 2*a(n-1) + 8, n>1, with a(0)=1, a(1)=2.
a(n) = 10*2^(n-1) - 8, n>=1, with a(0)=1.
E.g.f.: 5*exp(2*x) - 8*exp(x) + 4. - G. C. Greubel, Sep 08 2016
MATHEMATICA
Join[{1}, LinearRecurrence[{3, -2}, {2, 12}, 40]] (* Harvey P. Dale, Dec 30 2014 *)
Join[{1}, Table[5*2^n - 8, {n, 1, 25}]] (* G. C. Greubel, Sep 08 2016 *)
PROG
(PARI) Vec((1-x+8*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
EXTENSIONS
Two terms corrected by Johannes W. Meijer, May 26 2011
STATUS
approved