OFFSET
0,1
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..3300
Index entries for linear recurrences with constant coefficients, signature (4,-4).
FORMULA
a(n) = Sum_{k=0..n} (k+8)*binomial(n,k).
From R. J. Mathar, Apr 20 2009: (Start)
a(n) = (16+n)*2^(n-1).
a(n) = 4*a(n-1) - 4*a(n-2).
G.f.: (8-15*x)/(1-2*x)^2. (End)
E.g.f.: (x+8)*exp(2*x). - G. C. Greubel, Jun 02 2018
EXAMPLE
a(0)=8, a(1) = 2*8 + 1 = 17, a(2) = 2*17 + 2 = 36, a(3) = 2*36 + 4 = 76, a(4) = 2*76 + 8 = 160, ...
MATHEMATICA
LinearRecurrence[{4, -4}, {8, 17}, 30] (* or *) Table[(16+n)*2^(n-1), {n, 0, 30}] (* G. C. Greubel, Jun 02 2018 *)
PROG
(PARI) for(n=0, 30, print1((16+n)*2^(n-1), ", ")) \\ G. C. Greubel, Jun 02 2018
(Magma) [(16+n)*2^(n-1): n in [0..30]]; // G. C. Greubel, Jun 02 2018
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Philippe Deléham, Apr 20 2009
EXTENSIONS
More terms from R. J. Mathar, Apr 20 2009
STATUS
approved