login
A154252
Expansion of (1-x+8x^2)/((1-x)(1-2x)) .
4
1, 2, 12, 32, 72, 152, 312, 632, 1272, 2552, 5112, 10232, 20472, 40952, 81912, 163832, 327672, 655352, 1310712, 2621432, 5242872, 10485752, 20971512, 41943032, 83886072, 167772152, 335544312, 671088632, 1342177272, 2684354552, 5368709112, 10737418232
OFFSET
0,2
COMMENTS
Binomial transform of 1,1,9,1,9,1,9,1,9,1,9,1,9,1,9,...
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
KEYWORD
nonn,easy
AUTHOR
Philippe Deléham, Jan 05 2009
EXTENSIONS
Two terms corrected by Johannes W. Meijer, May 26 2011
STATUS
approved