|
|
A159696
|
|
a(0)=8, a(n) = 2*a(n-1) + 2^(n-1) for n > 0.
|
|
6
|
|
|
8, 17, 36, 76, 160, 336, 704, 1472, 3072, 6400, 13312, 27648, 57344, 118784, 245760, 507904, 1048576, 2162688, 4456448, 9175040, 18874368, 38797312, 79691776, 163577856, 335544320, 687865856, 1409286144, 2885681152, 5905580032
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,1
|
|
COMMENTS
|
|
|
LINKS
|
|
|
FORMULA
|
a(n) = Sum_{k=0..n} (k+8)*binomial(n,k).
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)
|
|
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
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|