OFFSET
0,1
COMMENTS
One of the diagonals of the n-th differences of A154383.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..150
Index entries for linear recurrences with constant coefficients, signature (8, -12).
FORMULA
a(n+1) = 6*a(n) - 10*2^n.
a(n) = 6*a(n) - 5*A020714(n+1).
G.f.: 2*(2 - 9*x)/((6*x-1)*(2*x-1)). - R. J. Mathar, May 21 2009
E.g.f.: (1/2)*( 5*exp(2*x) + 3*exp(6*x) ). - G. C. Greubel, Sep 16 2016
EXAMPLE
Sequence A154383 and its k-th iterated difference in the k-th row are
...1.....0.....4.....2.....16......8.....64.....32....256....128...1024.
..-1.....4....-2....14.....-8.....56....-32....224...-128....896...-512.
...5....-6....16...-22.....64....-88....256...-352...1024..-1408...4096.
.-11....22...-38....86...-152....344...-608...1376..-2432...5504..-9728.
..33...-60...124..-238....496...-952...1984..-3808...7936.-15232..31744.
.-93...184..-362...734..-1448...2936..-5792..11744.-23168..46976.-92672.
.277..-546..1096.-2182...4384..-8728..17536.-34912..70144.-139648.280576.
The sequence is the diagonal T(k,k+2) in this array.
MAPLE
MATHEMATICA
Table[5*2^(n-1)+3*6^n/2, {n, 0, 50}] (* Wesley Ivan Hurt, Nov 13 2013 *)
PROG
(Magma) [5*2^(n-1)+3*6^n/2: n in [0..40]]; // Vincenzo Librandi, Apr 28 2011
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Paul Curtz, Jan 09 2009
EXTENSIONS
Edited by R. J. Mathar, May 21 2009
STATUS
approved