A154407 a(n) = 5*2^(n-1) + 3*6^n/2.

4, 14, 64, 344, 1984, 11744, 70144, 420224, 2520064, 15117824, 90701824, 544200704, 3265183744, 19591061504, 117546287104, 705277558784, 4231665025024, 25389989494784, 152339935657984, 914039611326464, 5484237662715904

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

A154407:=n->5*2^(n-1)+3*6^n/2; seq(A154407(n), n=0..50); # Wesley Ivan Hurt, Nov 13 2013

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

Sequence in context: A341682 A242764 A356004 * A222467 A184265 A020041

Adjacent sequences: A154404 A154405 A154406 * A154408 A154409 A154410

Keyword

nonn,easy

Author

Paul Curtz, Jan 09 2009

Extensions

Edited by R. J. Mathar, May 21 2009

Status

approved